Posted by: SATYASRINIVAS | March 10, 2008

MBA Career Opportunities

Most degrees are obtained with the purpose of advancing your career prospects and job opportunities. The same is the case with an MBA degree; the only difference being that an MBA degree is considered as the most valuable post graduate degree in the world and has exciting career opportunities. People take the MBA program in order to further their careers in their current jobs or to get a better job on the basis of their MBA degree.

Even within your existing company and in your current job, you can notice the difference in your career prospects pre-MBA and post-MBA. With an MBA degree under their belt, employees have a whole new world opened up to them and are elevated to managerial positions on the strength of the additional abilities and knowledge gained through the MBA program. If you are looking for a change in careers, an MBA degree affords the following career opportunities:

Marketing: People who are in charge of marketing the goods or services of any organization need to be able to create effective marketing strategies and convey their message to people efficiently. An MBA program equips its students with theoretical knowledge as well as practical marketing skills, which can help in getting jobs in the marketing field. With the MBA degree, you can look to become no less than a product manager responsible for marketing.

Finance: Those in the field of finance need to be quick thinkers, have high energy levels to stay abreast of the financial markets, and most importantly, need to have patience to deal with clients and explain things to them. The finance courses in an MBA program are a great way to determine if you have what it takes to be a success in finance. If so, then there are a host of top jobs that you can get in this field.

Government Jobs: People often live with the misconception that an MBA degree is only good for business because of its very name. But it can be very useful for a career in a government agency. Such jobs usually require you to be a big thinker and to be a team player. All this and more is learned in an MBA program. Government agencies have since long had a reputation of giving reactive responses that do not much translate into action. To change this image, government agencies are increasingly on the lookout for people who are doers and not merely talkers. Thus, someone with an MBA degree could have many career prospects in a government job.

Personal Business: Those who have their own business are known to benefit tremendously from completing an MBA program. But what is even better is that an MBA degree can give you all the relevant skills and abilities needed to start your very own enterprise and become an entrepreneur, thus giving you tremendous career opportunities.

Non-profit Organizations: An MBA degree can open up many jobs for you in non-profit organizations. Most people with this degree or those who are still pursuing this degree, do not give much thought to jobs in the non-profit sector as it is regarded as a ‘waste’ of their skills and abilities. But on the contrary, this is one sector that could benefit a great deal from having more people with MBAs involved in non-profit. As for the MBA graduate, it can be very rewarding, both financially and emotionally, to see that your talents are making a positive difference in the lives of many people. You get the chance to work for a worthy cause, while at the same time furthering your own career.

This is just the tip of the iceberg as far as career opportunities for MBAs are concerned. Having an MBA degree gives you countless job opportunities, mostly in top level positions, and can help to further your career tremendously.

Posted by: SATYASRINIVAS | March 6, 2008

1000 English Proverbs and Sayings –

1. A bad beginning makes a bad ending.
2. A bad corn promise is better than a good lawsuit.
3. A bad workman quarrels with his tools.
4. A bargain is a bargain.
5. A beggar can never be bankrupt.
6. A bird in the hand is worth two in the bush.
7. A bird may be known by its song.
8. A black hen lays a white egg.
9. A blind leader of the blind.
10. A blind man would be glad to see.
11. A broken friendship may be soldered, but will never be sound.
12. A burden of one’s own choice is not felt.
13. A burnt child dreads the fire.
14. A cat in gloves catches no mice.
15. A city that parleys is half gotten.
16. A civil denial is better than a rude grant.
17. A clean fast is better than a dirty breakfast.
18. A clean hand wants no washing.
19. A clear conscience laughs at false accusations.
20. A close mouth catches no flies.
21. A cock is valiant on his own dunghill.
22. A cracked bell can never sound well.
23. A creaking door hangs long on its hinges.
24. A curst cow has short horns.
25. A danger foreseen is half avoided.
26. A drop in the bucket.
27. A drowning man will catch at a straw.
28. A fair face may hide a foul heart.
29. A fault confessed is half redressed.
30. A fly in the ointment.
31. A fool always rushes to the fore.
32. A fool and his money are soon parted.
33. A fool at forty is a fool indeed.
34. A fool may ask more questions in an hour than a wise man can answer in seven
years.
35. A fool may throw a stone into a well which a hundred wise men cannot pull out.
36. A fool’s tongue runs before his wit.
37. A forced kindness deserves no thanks.
38. A foul morn may turn to a fair day.
39. A fox is not taken twice in the same snare.
40. A friend in need is a friend indeed.
43. A friend is never known till needed.
42. A friend to all is a friend to none.
43. A friend’s frown is better than a foe’s smile.
44. A good anvil does not fear the hammer.
45. A good beginning is half the battle.
46. A good beginning makes a good ending.
47. A good deed is never lost.
48. A good dog deserves a good bone.
49. A good example is the best sermon.
50. A good face is a letter of recommendation.
51. A good Jack makes a good Jill.
52. A good marksman may miss.
53. A good name is better than riches.
54. A good name is sooner lost than won.
55. A good name keeps its lustre in the dark.
56. A good wife makes a good husband.
57. A great dowry is a bed full of brambles.
58. A great fortune is a great slavery.
59. A great ship asks deep waters.
60. A guilty conscience needs no accuser.
61. A hard nut to crack.
62. A heavy purse makes a light heart.
63. A hedge between keeps friendship green.
64. A honey tongue, a heart of gall.
65. A hungry belly has no ears.
66. A hungry man is an angry man.
67. A Jack of all trades is master of none.
68. A Joke never gains an enemy but often loses a friend.
69. A lawyer never goes to law himself.
70. A lazy sheep thinks its wool heavy.
71. A liar is not believed when he speaks the truth.
72. A lie begets a lie.
73. A light purse is a heavy curse.
74. A light purse makes a heavy heart.
75. A little body often harbours a great soul.
76. A little fire is quickly trodden out.
77. A man can die but once.
78. A man can do no more than he can.
79. A man is known by the company he keeps.
80. A man of words and not of deeds is like a garden full of weeds.
81. A miserly father makes a prodigal son.
82. A miss is as good as a mile.
83. A new broom sweeps clean.
84. A nod from a lord is a breakfast for a fool.
85. A penny saved is a penny gained.
86. A penny soul never came to twopence.
87. A quiet conscience sleeps in thunder.
88. A rolling stone gathers no moss.
89. A round peg in a square hole.
90. A shy cat makes a proud mouse.
91. A silent fool is counted wise.
92. A small leak will sink a great ship.
93. A soft answer turns away wrath.
94. A sound mind in a sound body.
95. A stitch in time saves nine.
96. A storm in a teacup.
97. A tattler is worse than a thief.
98. A thief knows a thief as a wolf knows a wolf.
99. A thief passes for a gentleman when stealing has made him rich.
100. A threatened blow is seldom given.
101. A tree is known by its fruit.
102. A wager is a fool’s argument.
103. A watched pot never boils.
104. A wise man changes his mind, a fool never will.
105. A wolf in sheep’s clothing.
106. A wonder lasts but nine days.
107. A word is enough to the wise.
108. A word spoken is past recalling.
109. Actions speak louder than words.
110. Adversity is a great schoolmaster.
111. Adversity makes strange bedfellows.
112. After a storm comes a calm.
113. After dinner comes the reckoning.
114. After dinner sit (sleep) a while, after supper walk a mile.
115. After rain comes fair weather.
116. After us the deluge.
117. Agues come on horseback, but go away on foot.
118. All are good lasses, but whence come the bad wives?
119. All are not friends that speak us fair.
120. All are not hunters that blow the horn.
121. All are not merry that dance lightly.
122. All are not saints that go to church.
123. All asses wag their ears.
124. All bread is not baked in one oven.
125. All cats are grey in the dark (in the night).
126. All covet, all lose.
127. All doors open to courtesy.
128. All is fish that comes to his net.
129. All is not lost that is in peril.
130. All is well that ends well.
131. All lay load on the willing horse.
132. All men can’t be first.
133. All men can’t be masters.
134. All promises are either broken or kept.
135. All roads lead to Rome .
136. All sugar and honey.
137. All that glitters is not gold.
138. All things are difficult before they are easy.
139. All truths are not to be told.
140. All work and no play makes Jack a dull boy.
141. “Almost” never killed a fly (was never hanged).
142. Among the blind the one-eyed man is king.
143. An apple a day keeps the doctor away.
144. An ass in a lion’s skin.
145. An ass is but an ass, though laden with gold.
146. An ass loaded with gold climbs to the top of the castle.
147. An empty hand is no lure for a hawk.
148. An empty sack cannot stand upright.
149. An empty vessel gives a greater sound than a full barrel.
150. An evil chance seldom comes alone.
151. An honest tale speeds best, being plainly told.
152. An hour in the morning is worth two in the evening.
153. An idle brain is the devil’s workshop.
154. An ill wound is cured, not an ill name.
155. An oak is not felled at one stroke.
156. An old dog barks not in vain.
157. An open door may tempt a saint.
158. An ounce of discretion is worth a pound of learning.
159. An ox is taken by the horns, and a man by the tongue.
160. An unfortunate man would be drowned in a teacup.
161. Anger and haste hinder good counsel.
162. Any port in a storm.
163. Appearances are deceitful.
164. Appetite comes with eating.
165. As drunk as a lord.
166. As innocent as a babe unborn.
167. As like as an apple to an oyster.
168. As like as two peas.
169. As old as the hills.
170. As plain as the nose on a man’s face.
171. As plain as two and two make four.
172. As snug as a bug in a rug .
173. As sure as eggs is eggs.
174. As the call, so the echo.
175. As the fool thinks, so the bell clinks.
176. As the old cock crows, so does the young.
177. As the tree falls, so shall it lie.
178. As the tree, so the fruit.
179. As welcome as flowers in May.
180. As welcome as water in one’s shoes.
181. As well be hanged for a sheep as for a lamb.
182. As you brew, so must you drink.
183. As you make your bed, so must you lie on it.
184. As you sow, so shall you reap.
185. Ask no questions and you will be told no lies.
186. At the ends of the earth.
187. Bacchus has drowned more men than Neptune .
188. Bad news has wings.
189. Barking does seldom bite.
190. Be slow to promise and quick to perform.
191. Be swift to hear, slow to speak.
192. Beauty is but skin-deep.
193. Beauty lies in lover’s eyes.
194. Before one can say Jack Robinson.
195. Before you make a friend eat a bushel of salt with him.
196. Beggars cannot be choosers.
197. Believe not all that you see nor half what you hear.
198. Best defence is offence.
199. Better a glorious death than a shameful life.
200. Better a lean peace than a fat victory.
201. Better a little fire to warm us, than a great one to burn us.
202. Better an egg today than a hen tomorrow.
203. Better an open enemy than a false friend.
204. Better be alone than in bad company.
205. Better be born lucky than rich.
206. Better be envied than pitied.
207. Better be the head of a dog than the tail of a lion.
208. Better deny at once than promise long.
209. Better die standing than live kneeling.
210. Better early than late.
211. Better give a shilling than lend a half-crown.
212. Better go to bed supperless than rise in debt.
213. Better late than never.
214. Better lose a jest than a friend.
215. Better one-eyed than stone-blind.
216. Better the devil you know than the devil you don’t.
217. Better the foot slip than the tongue.
218. Better to do well than to say well.
219. Better to reign in hell, than serve in heaven.
220. Better unborn than untaught.
221. Better untaught than ill-taught.
222. Between the cup and the lip a morsel may slip.
223. Between the devil and the deep (blue) sea.
224. Between two evils ’tis not worth choosing.
225. Between two stools one goes (falls) to the ground.
226. Between the upper and nether millstone.
227. Betwixt and between.
228. Beware of a silent dog and still water.
229. Bind the sack before it be full.
230. Birds of a feather flock together.
231. Blind men can judge no colours.
232. Blood is thicker than water.
233. Borrowed garments never fit well.
234. Brevity is the soul of wit.
235. Burn not your house to rid it of the mouse.
236. Business before pleasure.
237. By doing nothing we learn to do ill.
238. By hook or by crook.
239. By the street of ‘by-and-bye’ one arrives at the house of ‘Never’.
240. Calamity is man’s true touchstone.
241. Care killed the cat.
242. Catch the bear before you sell his skin.
243. Caution is the parent of safety.
244. Charity begins at home.
245. Cheapest is the dearest.
246. Cheek brings success.
247. Children and fools must not play with edged tools.
248. Children are poor men’s riches.
249. Choose an author as you choose a friend.
250. Christmas comes but once a year, (but when it comes it brings good cheer).
251. Circumstances alter cases.
252. Claw me, and I will claw thee.
253. Cleanliness is next to godliness.
254. Company in distress makes trouble less.
255. Confession is the first step to repentance.
256. Counsel is no command.
257. Creditors have better memories than debtors.
258. Cross the stream where it is shallowest.
259. Crows do not pick crow’s eyes.
260. Curiosity killed a cat.
261. Curses like chickens come home to roost.
262. Custom is a second nature.
263. Custom is the plague of wise men and the idol of fools.
264. Cut your coat according to your cloth.
265. Death is the grand leveller.
266. Death pays all debts.
267. Death when it comes will have no denial.
268. Debt is the worst poverty.
269. Deeds, not words.
270. Delays are dangerous.
271. Desperate diseases must have desperate remedies.
272. Diligence is the mother of success (good luck).
273. Diseases are the interests of pleasures.
274. Divide and rule.
275. Do as you would be done by.
276. Dog does not eat dog.
277. Dog eats dog.
278. Dogs that put up many hares kill none.
279. Doing is better than saying.
280. Don’t count your chickens before they are hatched.
281. Don’t cross the bridges before you come to them.
282. Don’t have thy cloak to make when it begins to rain.
283. Don’t keep a dog and bark yourself.
284. Don’t look a gift horse in the mouth.
285. Don’t put all your eggs in one basket.
286. Don’t sell the bear’s skin before you’ve caught it.
287. Don’t trouble trouble until trouble troubles you.
288. Don’t whistle (halloo) until you are out of the wood.
289. Dot your i’s and cross your t’s.
290. Draw not your bow till your arrow is fixed.
291. Drive the nail that will go.
292. Drunken days have all their tomorrow.
293. Drunkenness reveals what soberness conceals.
294. Dumb dogs are dangerous.
295. Each bird loves to hear himself sing.
296. Early to bed and early to rise makes a man healthy, wealthy and wise.
297. Easier said than done.
298. East or West � home is best.
299. Easy come, easy go.
300. Eat at pleasure, drink with measure.
301. Empty vessels make the greatest (the most) sound.
302. Enough is as good as a feast.
303. Envy shoots at others and wounds herself.
304. Even reckoning makes long friends.
305. Every ass loves to hear himself bray.
306. Every barber knows that.
307. Every bean has its black.
308. Every bird likes its own nest.
309. Every bullet has its billet.
310. Every country has its customs.
311. Every dark cloud has a silver lining.
312. Every day is not Sunday.
313. Every dog has his day.
314. Every dog is a lion at home.
315. Every dog is valiant at his own door.
316. Every Jack has his Jill.
317. Every man has a fool in his sleeve.
318. Every man has his faults.
319. Every man has his hobby-horse.
320. Every man is the architect of his own fortunes.
321. Every man to his taste.
322. Every miller draws water to his own mill.
323. Every mother thinks her own gosling a swan.
324. Every one’s faults are not written in their foreheads.
325. Every tub must stand on its own bottom.
326. Every white has its black, and every sweet its sour.
327. Every why has a wherefore.
328. Everybody’s business is nobody’s business.
329. Everything comes to him who waits.
330. Everything is good in its season.
331. Evil communications corrupt good manners.
332. Experience is the mother of wisdom.
333. Experience keeps a dear school, but fools learn in no other.
334. Experience keeps no school, she teaches her pupils singly.
335. Extremes meet.
336. Facts are stubborn things.
337. Faint heart never won fair lady.
338. Fair without, foul (false) within.
339. Fair words break no bones.
340. False friends are worse than open enemies.
341. Familiarity breeds contempt.
342. Far from eye, far from heart.
343. Fasting comes after feasting.
344. Faults are thick where love is thin.
345. Feast today and fast tomorrow.
346. Fine feathers make fine birds.
347. Fine words butter no parsnips.
348. First catch your hare.
349. First come, first served.
350. First deserve and then desire.
351. First think, then speak.
352. Fish and company stink in three days.
353. Fish begins to stink at the head.
354. Follow the river and you’ll get to the sea.
355. Fool’s haste is no speed.
356. Fools and madmen speak the truth.
357. Fools grow without watering.
358. Fools may sometimes speak to the purpose.
359. Fools never know when they are well.
360. Fools rush in where angels fear to tread.
361. For the love of the game.
362. Forbearance is no acquittance.
363. Forbidden fruit is sweet.
364. Forewarned is forearmed.
365. Fortune favours the brave (the bold).
366. Fortune is easily found, but hard to be kept.
367. Four eyes see more (better) than two.
368. Friends are thieves of time.
369. From bad to worse.
370. From pillar to post.
371. Gentility without ability is worse than plain beggary.
372. Get a name to rise early, and you may lie all day.
373. Gifts from enemies are dangerous.
374. Give a fool rope enough, and he will hang himself.
375. Give every man thy ear, but few thy voice.
376. Give him an inch and he’ll take an ell.
377. Give never the wolf the wether to keep.
378. Gluttony kills more men than the sword.
379. Go to bed with the lamb and rise with the lark.
380. Good clothes open all doors.
381. Good counsel does no harm.
382. Good health is above wealth.
383. Good masters make good servants.
384. Good words and no deeds.
385. Good words without deeds are rushes and reeds.
386. Gossiping and lying go hand in hand.
387. Grasp all, lose all.
388. Great barkers are no biters.
389. Great boast, small roast.
390. Great cry and little wool.
391. Great spenders are bad lenders.
392. Great talkers are great liars.
393. Great talkers are little doers.
394. Greedy folk have long arms.
395. Habit cures habit.
396. Half a loaf is better than no bread.
397. “Hamlet” without the Prince of Denmark.
398. Handsome is that handsome does.
399. Happiness takes no account of time.
400. Happy is he that is happy in his children.
401. Hard words break no bones.
402. Hares may pull dead lions by the beard.
403. Harm watch, harm catch.
404. Haste makes waste.
405. Hasty climbers have sudden falls.
406. Hate not at the first harm.
407. Hatred is blind, as well as love.
408. Hawks will not pick hawks’ eyes.
409. He begins to die that quits his desires.
410. He cannot speak well that cannot hold his tongue.
411. He carries fire in one hand and water in the other.
412. He dances well to whom fortune pipes.
413. He gives twice who gives in a trice.
414. He goes long barefoot that waits for dead man’s shoes.
415. He is a fool that forgets himself.
416. He is a good friend that speaks well of us behind our backs.
417. He is happy that thinks himself so.
418. He is lifeless that is faultless.
419. He is not fit to command others that cannot command himself.
420. He is not laughed at that laughs at himself first.
421. He is not poor that has little, but he that desires much.
422. He jests at scars that never felt a wound.
423. He knows best what good is that has endured evil.
424. He knows how many beans make five.
425. He knows much who knows how to hold his tongue.
426. He laughs best who laughs last.
427. He lives long that lives well.
428. He must needs swim that is held up by the chin.
429. He should have a long spoon that sups with the devil.
430. He smells best that smells of nothing.
431. He that comes first to the hill may sit where he will.
432. He that commits a fault thinks everyone speaks of it.
433. He that does you an i!i turn will never forgive you.
434. He that fears every bush must never go a-birding.
435. He that fears you present wiil hate you absent.
436. He that goes a borrowing, goes a sorrowing.
437. He that goes barefoot must not plant thorns.
438. He that has a full purse never wanted a friend.
439. He that has a great nose thinks everybody is speaking of it.
440. He that has an ill name is half hanged.
441. He that has no children knows not what love is.
442. He that has He head needs no hat.
443. He that has no money needs no purse.
444. He that is born to be hanged shall never be drowned.
445. He that is full of himself is very empty.
446. He that is ill to himself will be good to nobody.
447. He that is warm thinks all so.
448. He that knows nothing doubts nothing.
449. He that lies down with dogs must rise up with fleas.
450. He that lives with cripples learns to limp.
451. He that mischief hatches, mischief catches.
452. He that never climbed never fell.
453. He that once deceives is ever suspected.
454. He that promises too much means nothing.
455. He that respects not is not respected.
456. He that seeks trouble never misses.
457. He that serves everybody is paid by nobody.
458. He that serves God for money will serve the devil for better wages.
459. He that spares the bad injures the good.
460. He that talks much errs much.
461. He that talks much lies much.
462. He that will eat the kernel must crack the nut.
463. He that will not when he may, when he will he shall have nay.
464. He that will steal an egg will steal an ox.
465. He that will thrive, must rise at five.
466. He that would eat the fruit must climb the tree.
467. He that would have eggs must endure the cackling of hens.
468. He who is born a fool is never cured.
469. He who hesitates is lost.
470. He who likes borrowing dislikes paying.
471. He who makes no mistakes, makes nothing.
472. He who pleased everybody died before he was born.
473. He who says what he likes, shall hear what he doesn’t like.
474. He who would catch fish must not mind getting wet.
475. He who would eat the nut must first crack the shell.
476. He who would search for pearls must dive below.
477. He will never set the Thames on fire.
478. He works best who knows his trade.
479. Head cook and bottle-washer.
480. Health is not valued till sickness comes.
481. His money burns a hole in his pocket.
482. Honesty is the best policy.
483. Honey is not for the ass’s mouth.
484. Honey is sweet, but the bee stings.
485. Honour and profit lie not in one sack.
486. Honours change manners.
487. Hope is a good breakfast, but a bad supper.
488. Hope is the poor man’s bread.
489. Hunger breaks stone walls.
490. Hunger finds no fault with cookery.
491. Hunger is the best sauce.
492. Hungry bellies have no ears.
493. Idle folks lack no excuses.
494. Idleness is the mother of all evil.
495. Idleness rusts the mind.
496. If an ass (donkey) bray at you, don’t bray at him.
497. If ifs and ans were pots and pans…
498. If my aunt had been a man, she’d have been my uncle.
499. If the blind lead the blind, both shall fall into the ditch.
500. If the sky falls, we shall catch larks.
501. If there were no clouds, we should not enjoy the sun.
502. If things were to be done twice all would be wise.
503. If we can’t as we would, we must do as we can.
504. If wishes were horses, beggars might ride.
505. If you agree to carry the calf, they’ll make you carry the cow.
506. If you cannot bite, never show your teeth.
507. If you cannot have the best, make the best of what you have.
508. If you dance you must pay the fiddler.
509. If you laugh before breakfast you’ll cry before supper.
510. If you run after two hares, you will catch neither.
511. If you sell the cow, you sell her milk too.
512. If you throw mud enough, some of it will stick.
513. If you try to please all you will please none.
514. If you want a thing well done, do it yourself.
515. Ill-gotten gains never prosper.
516. Ill-gotten, ill-spent.
517. In every beginning think of the end.
518. In for a penny, in for a pound.
519. In the country of the blind one-eyed man is a king.
520. In the end things will mend.
521. In the evening one may praise the day.
522. Iron hand (fist) in a velvet glove.
523. It is a good horse that never stumbles.
524. It is a long lane that has no turning.
525. It is a poor mouse that has only one hole.
526. It is an ill bird that fouls its own nest.
527. It is an ill wind that blows nobody good.
528. It is a silly fish, that is caught twice with the same bait.
529. It is easy to swim if another hoids up your chin (head).
530. It is enough to make a cat laugh.
531. It is good fishing in troubled waters.
532. It is never too late to learn.
533. It is no use crying over spilt milk.
534. It is the first step that costs.
535. It never rains but it pours.
536. It’s as broad as it’s long.
537. It’s no use pumping a dry well.
538. It’s one thing to flourish and another to fight.
539. It takes all sorts to make a world.
540. Jackdaw in peacock’s feathers.
541. Jest with an ass and he will flap you in the face with his tail.
542. Judge not of men and things at first sight.
543. Just as the twig is bent, the tree is inclined.
544. Keep a thing seven years and you will find a use for it.
545. Keep your mouth shut and your ears open.
546. Keep your mouth shut and your eyes open.
547. Last, but not least.
548. Laws catch flies, but let hornets go free.
549. Learn to creep before you leap.
550. Learn to say before you sing.
551. Learn wisdom by the follies of others.
552. Least said, soonest mended.
553. Leaves without figs.
554. Let bygones be bygones.
555. Let every man praise the bridge he goes over.
556. Let sleeping dogs lie.
557. Let well (enough) alone.
558. Liars need good memories.
559. Lies have short legs.
560. Life is but a span.
561. Life is not a bed of roses.
562. Life is not all cakes and ale (beer and skittles).
563. Like a cat on hot bricks.
564. Like a needle in a haystack.
565. Like begets like.
566. Like cures like.
567. Like father, like son.
568. Like draws to like.
569. Like master, like man.
570. Like mother, like daughter.
571. Like parents, like children.
572. Like priest, like people.
573. Like teacher, like pupil.
574. Little chips light great fires.
575. Little knowledge is a dangerous thing.
576. Little pigeons can carry great messages.
577. Little pitchers have long ears.
578. Little strokes fell great oaks.
579. Little thieves are hanged, but great ones escape.
580. Little things amuse little minds.
581. Live and learn.
582. Live and let live.
583. Live not to eat, but eat to live.
584. Long absent, soon forgotten.
585. Look before you leap.
586. Look before you leap, but having leapt never look back.
587. Lookers-on see more than players.
588. Lord (God, Heaven) helps those (them) who help themselves.
589. Lost time is never found again.
590. Love cannot be forced.
591. Love in a cottage.
592. Love is blind, as well as hatred.
593. Love me, love my dog.
594. Love will creep where it may not go.
595. Make haste slowly.
596. Make hay while the sun shines.
597. Make or mar.
598. Man proposes but God disposes.
599. Many a fine dish has nothing on it.
600. Many a good cow has a bad calf.
601. Many a good father has but a bad son.
602. Many a little makes a mickle.
603. Many a true word is spoken in jest.
604. Many hands make light work.
605. Many men, many minds.
606. Many words hurt more than swords.
607. Many words will not fill a bushel.
608. Marriages are made in heaven.
609. Measure for measure.
610. Measure thrice and cut once.
611. Men may meet but mountains never.
612. Mend or end (end or mend).
613. Might goes before right.
614. Misfortunes never come alone (singly).
615. Misfortunes tell us what fortune is.
616. Money begets money.
617. Money has no smell.
618. Money is a good servant but a bad master.
619. Money often unmakes the men who make it.
620. Money spent on the brain is never spent in vain.
621. More haste, less speed.
622. Much ado about nothing.
623. Much will have more.
624. Muck and money go together.
625. Murder will out.
626. My house is my castle.
627. Name not a rope in his house that was hanged.
628. Necessity is the mother of invention.
629. Necessity knows no law.
630. Neck or nothing.
631. Need makes the old wife trot.
632. Needs must when the devil drives.
633. Neither fish nor flesh.
634. Neither here nor there.
635. Neither rhyme nor reason.
636. Never cackle till your egg is laid.
637. Never cast dirt into that fountain of which you have sometime drunk.
638. Never do things by halves.
639. Never fry a fish till it’s caught.
640. Never offer to teach fish to swim.
641. Never put off till tomorrow what you can do (can be done) today.
642. Never quit certainty for hope.
643. Never too much of a good thing.
644. Never try to prove what nobody doubts.
645. Never write what you dare not sign.
646. New brooms sweep clean.
647. New lords, new laws.
648. Nightingales will not sing in a cage.
649. No flying from fate.
650. No garden without its weeds.
651. No great loss without some small gain.
652. No herb will cure love.
653. No joy without alloy.
654. No living man all things can.
655. No longer pipe, no longer dance.
656. No man is wise at all times.
657. No man loves his fetters, be they made of gold.
658. No news (is) good news.
659. No pains, no gains.
660. No song, no supper.
661. No sweet without (some) sweat.
662. No wisdom like silence.
663. None but the brave deserve the fair.
664. None so blind as those who won’t see.
665. None so deaf as those that won’t hear.
666. Nothing comes out of the sack but what was in it.
667. Nothing is impossible to a willing heart.
668. Nothing must be done hastily but killing of fleas.
669. Nothing so bad, as not to be good for something.
670. Nothing succeeds like success.
671. Nothing venture, nothing have.
672. Oaks may fall when reeds stand the storm.
673. Of two evils choose the least.
674. Old birds are not caught with chaff.
675. Old friends and old wine are best.
676. On Shank’s mare.
677. Once bitten, twice shy.
678. Once is no rule (custom).
679. One beats the bush, and another catches the bird.
680. One chick keeps a hen busy.
681. One drop of poison infects the whole tun of wine.
682. One fire drives out another.
683. One good turn deserves another.
684. One law for the rich, and another for the poor.
685. One lie makes many.
686. One link broken, the whole chain is broken.
687. One man, no man.
688. One man’s meat is another man’s poison.
689. One scabby sheep will mar a whole flock.
690. One swallow does not make a summer.
691. One today is worth two tomorrow.
692. Open not your door when the devil knocks.
693. Opinions differ.
694. Opportunity makes the thief.
695. Out of sight, out of mind.
696. Out of the frying-pan into the fire.
697. Packed like herrings.
698. Patience is a plaster for all sores.
699. Penny-wise and pound-foolish.
700. Pleasure has a sting in its tail.
701. Plenty is no plague.
702. Politeness costs little (nothing), but yields much.
703. Poverty is no sin.
704. Poverty is not a shame, but the being ashamed of it is.
705. Practise what you preach.
706. Praise is not pudding.
707. Pride goes before a fall.
708. Procrastination is the thief of time.
709. Promise is debt.
710. Promise little, but do much.
711. Prosperity makes friends, and adversity tries them.
712. Put not your hand between the bark and the tree.
713. Rain at seven, fine at eleven.
714. Rats desert a sinking ship.
715. Repentance is good, but innocence is better.
716. Respect yourself, or no one else will respect you.
717. Roll my log and I will roll yours.
718. Rome was not built in a day.
719. Salt water and absence wash away love.
720. Saying and doing are two things.
721. Score twice before you cut once.
722. Scornful dogs will eat dirty puddings.
723. Scratch my back and I’ll scratch yours.
724. Self done is soon done.
725. Self done is well done.
726. Self is a bad counsellor.
727. Self-praise is no recommendation.
728. Set a beggar on horseback and he’ll ride to the devil.
729. Set a thief to catch a thief.
730. Shallow streams make most din.
731. Short debts (accounts) make long friends.
732. Silence gives consent.
733. Since Adam was a boy.
734. Sink or swim!
735. Six of one and half a dozen of the other.
736. Slow and steady wins the race.
737. Slow but sure.
738. Small rain lays great dust.
739. So many countries, so many customs.
740. So many men, so many minds.
741. Soft fire makes sweet malt.
742. Something is rotten in the state of Denmark.
743. Soon learnt, soon forgotten.
744. Soon ripe, soon rotten.
745. Speak (talk) of the devil and he will appear (is sure to appear).
746. Speech is silver but silence is gold.
747. Standers-by see more than gamesters.
748. Still waters run deep.
749. Stolen pleasures are sweetest.
750. Stretch your arm no further than your sleeve will reach.
751. Stretch your legs according to the coverlet.
752. Strike while the iron is hot.
753. Stuff today and starve tomorrow.
754. Success is never blamed.
755. Such carpenters, such chips.
756. Sweep before your own door.
757. Take care of the pence and the pounds will take care of themselves.
758. Take us as you find us.
759. Tarred with the same brush.
760. Tastes differ.
761. Tell that to the marines.
762. That cock won’t fight.
763. That which one least anticipates soonest comes to pass.
764. That’s a horse of another colour.
765. That’s where the shoe pinches!
766. The beggar may sing before the thief (before a footpad).
767. The best fish smell when they are three days old.
768. The best fish swim near the bottom.
769. The best is oftentimes the enemy of the good.
770. The busiest man finds the most leisure.
771. The camel going to seek horns lost his ears.
772. The cap fits.
773. The cask savours of the first fill.
774. The cat shuts its eyes when stealing cream.
775. The cat would eat fish and would not wet her paws.
776. The chain is no stronger than its weakest link.
777. The cobbler should stick to his last.
778. The cobbler’s wife is the worst shod.
779. The darkest hour is that before the dawn.
780. The darkest place is under the candlestick.
781. The devil is not so black as he is painted.
782. The devil knows many things because he is old.
783. The devil lurks behind the cross.
784. The devil rebuking sin.
785. The dogs bark, but the caravan goes on.
786. The Dutch have taken Holland !
787. The early bird catches the worm.
788. The end crowns the work.
789. The end justifies the means.
790. The evils we bring on ourselves are hardest to bear.
791. The exception proves the rule.
792. The face is the index of the mind.
793. The falling out of lovers is the renewing of love.
794. The fat is in the fire.
795. The first blow is half the battle.
796. The furthest way about is the nearest way home.
797. The game is not worth the candle.
798. The heart that once truly loves never forgets.
799. The higher the ape goes, the more he shows his tail.
800. The last drop makes the cup run over.
801. The last straw breaks the camel’s back.
802. The leopard cannot change its spots.
803. The longest day has an end.
804. The mill cannot grind with the water that is past.
805. The moon does not heed the barking of dogs.
806. The more haste, the less speed.
807. The more the merrier.
808. The morning sun never lasts a day.
809. The mountain has brought forth a mouse.
810. The nearer the bone, the sweeter the flesh.
811. The pitcher goes often to the well but is broken at last.
812. The pot calls the kettle black.
813. The proof of the pudding is in the eating.
814. The receiver is as bad as the thief.
815. The remedy is worse than the disease.
816. The rotten apple injures its neighbours.
817. The scalded dog fears cold water.
818. The tailor makes the man.
819. The tongue of idle persons is never idle.
820. The voice of one man is the voice of no one.
821. The way (the road) to hell is paved with good intentions.
822. The wind cannot be caught in a net.
823. The work shows the workman.
824. There are lees to every wine.
825. There are more ways to the wood than one.
826. There is a place for everything, and everything in its place.
827. There is more than one way to kill a cat.
828. There is no fire without smoke.
829. There is no place like home.
830. There is no rose without a thorn.
831. There is no rule without an exception.
832. There is no smoke without fire.
833. There’s many a slip ‘tween (== between) the cup and the lip.
834. There’s no use crying over spilt milk.
835. They are hand and glove.
836. They must hunger in winter that will not work in summer.
837. Things past cannot be recalled.
838. Think today and speak tomorrow.
839. Those who live in glass houses should not throw stones.
840. Time and tide wait for no man.
841. Time cures all things.
842. Time is money.
843. Time is the great healer.
844. Time works wonders.
845. To add fuel (oil) to the fire (flames).
846. To angle with a silver hook.
847. To be born with a silver spoon in one’s mouth.
848. To be head over ears in debt.
849. To be in one’s birthday suit.
850. To be up to the ears in love.
851. To be wise behind the hand.
852. To beat about the bush.
853. To beat the air.
854. To bring grist to somebody’s mill.
855. To build a fire under oneself.
856. To buy a pig in a poke.
857. To call a spade a spade.
858. To call off the dogs.
859. To carry coals to Newcastle.
860. To cast pearls before swine.
861. To cast prudence to the winds.
862. To come away none the wiser.
863. To come off cheap.
864. To come off with a whole skin.
865. To come off with flying colours.
866. To come out dry.
867. To come out with clean hands.
868. To cook a hare before catching him.
869. To cry with one eye and laugh with the other.
870. To cut one’s throat with a feather.
871. To draw (pull) in one’s horns.
872. To drop a bucket into an empty well.
873. To draw water in a sieve.
874. To eat the calf in the cow’s belly.
875. To err is human.
876. To fiddle while Rome is burning.
877. To fight with one’s own shadow.
878. To find a mare’s nest.
879. To fish in troubled waters.
880. To fit like a glove.
881. To flog a dead horse.
882. To get out of bed on the wrong side.
883. To give a lark to catch a kite.
884. To go for wool and come home shorn.
885. To go through fire and water (through thick and thin).
886. To have a finger in the pie.
887. To have rats in the attic.
888. To hit the nail on the head.
889. To kick against the pricks.
890. To kill two birds with one stone.
891. To know everything is to know nothing.
892. To know on which side one’s bread is buttered.
893. To know what’s what.
894. To lay by for a rainy day.
895. To live from hand to mouth.
896. To lock the stable-door after the horse is stolen.
897. To look for a needle in a haystack.
898. To love somebody (something) as the devil loves holy water.
899. To make a mountain out of a molehill.
900. To make both ends meet.
901. To make the cup run over.
902. To make (to turn) the air blue.
903. To measure another man’s foot by one’s own last.
904. To measure other people’s corn by one’s own bushel.
905. To pay one back in one’s own coin.
906. To plough the sand.
907. To pour water into a sieve.
908. To pull the chestnuts out of the fire for somebody.
909. To pull the devil by the tail.
910. To put a spoke in somebody’s wheel.
911. To put off till Doomsday.
912. To put (set) the cart before the horse.
913. To rob one’s belly to cover one’s back.
914. To roll in money.
915. To run with the hare and hunt with the hounds.
916. To save one’s bacon.
917. To send (carry) owls to Athens.
918. To set the wolf to keep the sheep.
919. To stick to somebody like a leech.
920. To strain at a gnat and swallow a camel.
921. To take counsel of one’s pillow.
922. To take the bull by the horns.
923. To teach the dog to bark.
924. To tell tales out of school.
925. To throw a stone in one’s own garden.
926. To throw dust in somebody’s eyes.
927. To throw straws against the wind.
928. To treat somebody with a dose of his own medicine.
929. To use a steam-hammer to crack nuts.
930. To wash one’s dirty linen in public.
931. To wear one’s heart upon one’s sleeve.
932. To weep over an onion.
933. To work with the left hand.
934. Tomorrow come never.
935. Too many cooks spoil the broth.
936. Too much knowledge makes the head bald.
937. Too much of a good thing is good for nothing.
938. Too much water drowned the miller .
939. Too swift arrives as tardy as too slow.
940. True blue will never stain.
941. True coral needs no painter’s brush.
942. Truth comes out of the mouths of babes and sucklings.
943. Truth is stranger than fiction.
944. Truth lies at the bottom of a well.
945. Two blacks do not make a white.
946. Two heads are better than one.
947. Two is company, but three is none.
948. Velvet paws hide sharp claws.
949. Virtue is its own reward.
950. Wait for the cat to jump.
951. Walls have ears.
952. Wash your dirty linen at home.
953. Waste not, want not.
954. We know not what is good until we have lost it.
955. We never know the value of water till the well is dry.
956. We shall see what we shall see.
957. We soon believe what we desire.
958. Wealth is nothing without health.
959. Well begun is half done.
960. What can’t be cured, must be endured.
961. What is bred in the bone will not go out of the flesh.
962. What is done by night appears by day.
963. What is done cannot be undone.
964. What is got over the devil’s back is spent under his belly.
965. What is lost is lost.
966. What is sauce for the goose is sauce for the gander.
967. What is worth doing at alt is worth doing well.
968. What must be, must be.
969. What the heart thinks the tongue speaks.
970. What we do willingly is easy.
971. When angry, count a hundred.
972. When at Rome, do as the Romans do.
973. When children stand quiet, they have done some harm.
974. When flatterers meet, the devil goes to dinner.
975. When guns speak it is too late to argue.
976. When pigs fly.
977. When Queen Anne was alive.
978. When the cat is away, the mice will play.
979. When the devil is blind.
980. When the fox preaches, take care of your geese.
981. When the pinch comes, you remember the old shoe.
982. When three know it, alt know it.
983. When wine is in wit is out.
984. Where there’s a will, there’s a way.
985. While the grass grows the horse starves.
986. While there is life there is hope.
987. Who breaks, pays.
988. Who has never tasted bitter, knows not what is sweet.
989. Who keeps company with the wolf, will learn to howl.
990. Wise after the event.
991. With time and patience the leaf of the mulberry becomes satin.
992. Words pay no debts.
993. You can take a horse to the water but you cannot make him drink.
994. You cannot eat your cake and have it.
995. You cannot flay the same ox twice.
996. You cannot judge a tree by it bark.
997. You cannot teach old dogs new tricks.
998. You cannot wash charcoal white.
999. You made your bed, now lie in it.
1000. Zeal without knowledge is a runaway horse.

Posted by: SATYASRINIVAS | July 5, 2007

Black google

More commonly known as Blackle, this search engine is exactly like Google, except, (as all of you might have guessed) is black. How does this help the environment? It saves power.When appearing on your screen, a black page uses around 15 watts less than a white page would. Google, being white, therefore uses more power than Blackle. It is said that Google gets 200 million hits a day. Just imagine if even a quarter of those users switched over to Blackle, how much energy would be saved?

So think about it, it takes the same amount of time and effort for you but you save power. What’s your decision? Blackle or Google?

Posted by: SATYASRINIVAS | July 5, 2007

a man in love

A man in love has a smile on his face,
A man in love is used to disgrace,
A man in love cares , not for the world,
For a man in love, his love is his world.
A man in love takes sorrow with pride,
A man in love his feelings he cant hide,
A man in love sees joy in defeat,
A man in love knows , no surrender , no retreat.

A man in love is ever content,
A man in love breeds no contempt,
A man in love is the one to trust,
A man in love is always just.

A man in love has conquered it all,
A man in love knows no vices at all,
But a man in loved when once betrayed,
Will burn the world with fire enraged

Posted by: SATYASRINIVAS | July 5, 2007

quotes

Miles and Miles apart that
lies between us
there’s never a time I don’t stop thinking about you,
All night I lie awake and think about what it would be like to feel your lips against mine,
Can you dream of me the way I dream of you?
there will be that day
that day of meeting each other
the joy of happiness that will stream down our faces when we are holding each other tightly,
every time I talk to you
my body is singing with butterflies,
through miles and miles apart
life holds us patience
there will be that day
when its just me and you
living in the arms of each other
i promise you
through miles and miles apart
that beautiful day of us being together…will come.
Love is an ideal thing, marriage a real thing; a confusion of the real with the ideal never goes unpunished. – Goethe.

A man falls in love through his eyes, a woman through her ears. – Woodrow Wyatt

I like not only to be loved, but to be told that I am loved. – George Elliot

LOVE: The irresistable desire to be irresistibly desired. – Mark Twain

The first duty of love – is to listen. – Paul Tillich

One word frees us of all the weight and pain in life. That word is love. – Sophocles

How on earth are you ever going to explain in terms of chemistry and physics so important a biological phenomenon as first love?” – Albert Einstien

Life is a flower of which love is the honey. – Victor Hugo

Love is friendship set to music. – E. Joseph Crossmann

At the touch of love, everyone becomes a poet. – Plato

Love is a great beautifier. – Louisa May Alcott

In our life there is a single color, as on an artist`s palette, which provides the meaning of life and art. It is the color of love. – Marc Chagall

Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. THAT’S relativity. – Einstein.

I feel something in my heart, it’s like a little flame, every time I see you, this flame lights up, this flame is special for you, because I LOVE YOU!

Love is being stupid together.

Love is not just looking at each other, it’s looking in the same direction.

Never frown, even when you are sad, because you never know who is falling in love with your smile.

No one is too young for love, because love doesn’t come from your mind, which knows your age, but from your heart, which knows no age.

Love conquers all. – Virgil.
…………………………………………………………………..
Never live in the past but always learn from it.
       – unknown
He who knows all the answers has not yet been asked all the questions.
       – unknown
Wisdom is supreme; therefore make a full effort to get wisdom.
Esteem her and she will exalt your; embrace her and she will honor you.
       – Proverbs 4:7-8
Education is the power to think clearly, the power to act well in the world’s work, and the power to appreciate life.
       – Brigham Young
The sublimity of wisdom is to do those things living that are desired when dying.
       – unknown
The foolish man seeks happiness in the distance, the wise grows it under his feet.
       – James Oppenheim
The wisest mind has something yet to learn.
       – George Santayana
The secret of health for both mind and body is not to mourn for the past, worry about the future, or anticipate troubles but to live in the present moment wisely and earnestly.
       – Buddha
Luck is what happens when preparation meets opportunity.
       – Darrell Royal, in James A. Michener, Sports in America, 1976.
Do not believe in anything simply because you have heard it.
Do not believe in anything simply because it is spoken and rumored by many.
Do not believe in anything simply because it is found written in your religious books.
Do not believe in anything merely on the authority of your teachers and elders.
Do not believe in traditions because they have been handed down for many generations.
But after observation and analysis, when you find that anything agrees with reason and is conducive to the good and benefit of one and all, then accept it and live up to it.
       – Buddha
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

Posted by: SATYASRINIVAS | July 5, 2007

Dr. Abdul Kalaam’s Speech

Dr. Abdul Kalaam’s Speech

I have three visions for India.

In 3000 years of our history people from all over the world have come and
invaded us, captured our lands, conquered our minds. From Alexander onwards.
The Greeks, the Turks, the Moguls, the Portuguese, the British, the French, the
Dutch, all of them came and looted us, took over what was ours.

Yet we have not done this to any other nation. We have not conquered anyone. We
have not grabbed their land, their culture, and their history and tried to
enforce our way of life on them. Why? Because we respect the freedom of others.
That is why my first vision is that of FREEDOM. I believe that India got its
first vision of this in 1857, when we started the war of independence. It is
this freedom that we must protect and nurture and build on. If we are not free,
no one will respect us.

My second vision for India is DEVELOPMENT. For fifty years we have been a
developing nation. It is time we see ourselves as a developed nation. We are
among top 5 nations of the world in terms of GDP. We have 10 percent growth
rate in most areas. Our poverty levels are falling. Our achievements are being
globally recognized today. Yet we lack the self-confidence to see ourselves as
a developed nation, self-reliant and self-assured. Isn’t this incorrect?

I have a THIRD vision. India must STAND UP to the world. Because I believe that
unless India stands up to the world, no one will respect us. Only strength
respects strength. We must be strong not only as a military power but also as
an economic power. Both must go hand-in-hand.

My good fortune was to have worked with three great minds. Dr.Vikram Sarabhai
of the Dept. of space, Professor Satish Dhawan, who succeeded him and Dr. Brahm
Prakash, father of nuclear material. I was lucky to have worked with all three
of them closely and consider this the great opportunity of my life.

I see four milestones in my career:

ONE: Twenty years I spent in ISRO. I was given the opportunity to be the
project director for India’s first satellite launch vehicle, SLV3. The one that
launched Rohini. These years played a very important role in my life of
Scientist.

TWO: After my ISRO years, I joined DRDO and got a chance to be the part of
India’s guided missile program. It was my second bliss when Agni met its
mission requirements in 1994.

THREE: The Dept. of Atomic Energy and DRDO had this tremendous partnership in
the recent nuclear tests, on May 11 and 13. This was the third bliss. The joy
of participating with my team in these nuclear tests and proving to the world
that India can make it, that we are no longer a developing nation but one of
them. It made me feel very proud as an Indian. The fact that we have now
developed for Agni a re-entry structure, for which we have developed this new
material. A Very light material called carbon-carbon.

FOUR: One day an orthopaedic surgeon from Nizam Institute of Medical Sciences
visited my laboratory. He lifted the material and found it so light that he
took me to his hospital and showed me his patients. There were these little
girls and boys with heavy metallic calipers weighing over three Kg. each,
dragging their feet around. He said to me: Please remove the pain of my
patients. In three weeks, we made these Floor reaction Orthosis 300 gram
callipers and took them to the orthopedic centre. The children didn’t believe
their eyes. From dragging around a three kg load on their legs, they could now
move around! Their parents had tears in their eyes. That was my fourth bliss!

Why is the media here so negative? Why are we in India so embarrassed to
recognize our own strengths, our achievements? We are such a great nation. We
have so many amazing success stories but we refuse to acknowledge them.

Why? We are the first in milk production. We are number one in Remote sensing
satellites. We are the second largest producer of wheat. We are the second
largest producer of rice. Look at Dr. Sudarshan; he has transferred the tribal
village into a self-sustaining, self-driving unit. There are millions of such
achievements but our media is only obsessed in the bad news and failures and
disasters.

I was in Tel Aviv once and I was reading the Israeli newspaper. It was the day
after a lot of attacks and bombardments and deaths had taken place. The Hamas
had struck. But the front page of the newspaper had the picture of a Jewish
gentleman who in five years had transformed his desert land into an orchid and
a granary. It was this inspiring picture that everyone woke up to. The gory
details of killings, bombardments, deaths, were inside in the newspaper, buried
among other news. In India we only read about death, sickness, terrorism,
crime. Why are we so NEGATIVE?

Another question: Why are we, as a nation so obsessed with foreign things? We
want foreign TVs. We want foreign shirts. We want foreign technology. Why this
obsession with everything imported. Do we not realize that self-respect comes
with self-reliance? I was in Hyderabad giving this lecture, when a 14 years old
girl asked me for my autograph. I asked her what her goal in life is: She
replied: I want to live in a developed India. For her, you and I will have to
build this developed India. You must proclaim. India is not an under-developed
nation; it is a highly developed nation.

Do you have 10 minutes?

Allow me to come back with vengeance. Got 10 minutes for your country? If yes,
then read; otherwise, choice is yours. YOU say that our government is
inefficient. YOU say that our laws are too old. YOU say that the municipality
does not pick up the garbage. YOU say that the phones don’t work, the railways
are a joke, the airline is the worst in the world, and mails never reach their
destination. YOU say that our country has been fed to the dogs and is the
absolute pits. YOU say, say and say. What do YOU do about it?

Take a person on his way to Singapore. Give him a name – YOURS. Give him a face
– YOURS. YOU walk out of the airport and you are at your International best. In
Singapore you don’t throw cigarette butts on the roads or eat in the stores.
YOU are as proud of their Underground Links as they are. You pay $5 (approx.
Rs.60) to drive through Orchard Road (equivalent of Mahim causeway or Pedder
Road) between 5 PM and 8 PM. YOU comeback to the parking lot to punch your
parking ticket if you have over stayed in a restaurant or a shopping mall
irrespective of your status identity.

In Singapore you don’t say anything, DO YOU? YOU wouldn’t dare to eat in public
during Ramadan, in Dubai. YOU would not dare to go out without your head
covered in Jeddah. YOU would not dare to buy an employee of the telephone
exchange in London at 10 pounds (Rs.650) a month to, “see to it that my STD and
ISD calls are billed to someone else. ” YOU would not dare to speed beyond 55
mph (88 kmph) in Washington and then tell the traffic
cop, “Jaanta hai sala main kaun hoon (Do you know who I am?). I am so and so’s
son. Take your two bucks and get lost.” YOU wouldn’t chuck an empty coconut
shell anywhere other than the garbage pail on the beaches in Australia and New
Zealand. Why don’t YOU spit Paan on the streets of Tokyo? Why don’t YOU use
examination jockeys or buy fake certificates in Boston? We are still talking of
the same YOU. YOU who can respect and conform to a foreign system in other
countries but cannot in your own. You who will throw papers and cigarettes on
the road the moment you touch Indian ground. You can be an involved and
appreciative citizen in an alien country why cannot you be the same here in
India.

Once in an interview, the famous Ex-municipal commissioner of Bombay
Mr.Tinaikar had a point to make. “Rich people’s dogs are walked on the streets
to leave their affluent droppings all over the place,” he said. “And then the
same people turn around to criticize and blame the authorities for inefficiency
and dirty pavements. What do they expect the officers to do? Go down with a
broom every time their dog feels the pressure in his bowels? In America every
dog owner has to clean up after his pet has done the job. Same in Japan. Will
the Indian citizen do that here?”

He’s right. We go to the polls to choose a government and after that forfeit
all responsibility. We sit back wanting to be pampered and expect the
government to do everything for us whilst our contribution is totally negative.
We expect the government to clean up but we are not going to stop chucking
garbage all over the place or are we going to stop to pick a up a stray piece
of paper and throw it in the bin. We expect the railways to provide clean
bathrooms but we are not going to learn the proper use of bathrooms. We want
Indian Airlines and Air India to provide the best of food and toiletries but we
are not going to stop pilfering at the least opportunity. This applies even to
the staff who is known not to pass on the service to the public. When it comes
to burning social issues like those related to women, dowry, girl child and
others, we make loud drawing room protestations and continue to do the reverse
at home. Our excuse?

“It’s the whole system which has to change, how will it matter if I alone
forego my sons’ rights to a dowry.”

So who’s going to change the system? What does a system consist of? Very
conveniently for us it consists of our neighbors, other households, other
cities, other communities and the government.

But definitely not me and YOU.

When it comes to us actually making a positive contribution to the system we
lock ourselves along with our families into a safe cocoon and look into the
distance at countries far away and wait for a Mr. Clean to come along & work
miracles for us with a majestic sweep of his hand.

Or we leave the country and run away. Like lazy cowards hounded by our fears we
run to America to bask in their glory and praise their system. When New York
becomes insecure we run to England. When England experiences unemployment, we
take the next flight out to the Gulf. When the Gulf is war struck, we demand to
be rescued and brought home by the Indian government.

Everybody is out to abuse and rape the country. Nobody thinks of feeding the
system. Our conscience is mortgaged to money.

Dear Indians, The article is highly thought inductive, calls for a great deal
of introspection and pricks one’s conscience too…. I am echoing J.F.
Kennedy’s words to his fellow Americans to relate to Indians.
“ASK WHAT WE CAN DO FOR INDIA AND DO WHAT HAS TO BE DONE TO MAKE INDIA WHAT
AMERICA AND OTHER WESTERN COUNTRIES ARE TODAY”
End of Speech

Lets do what India needs from us. Forward this mail to each Indian.

Posted by: SATYASRINIVAS | June 4, 2007

APTITUDE2

1) What is the average speed of the car ?

a) The car covered 25% of distance at 45 Km per Hour.
b) The car covered the remaining 75% of distance at 55 Km /
Hour.
Let the total distance be 100X
Time taken for first 25x = 25X/45
Time taken to cover remaining 75X = 75X/55
Total time taken = 25X/45 + 75X/55 =
LCM of 45 and 55 = 495
= 275X+675X/ 495 = 950X/495
So average speed = 100X/ ( 950X/495) = 49500/950 Km per
hour.

————————————————————————-

2)What is the remainder when factorial 11 divided by 17 ?

 

11*10*9*8*7*6*5*4*3*2 Mod 17
11*10 Mod 17 = 8
9*8 Mod 17= 4
7*6 Mod 17= 8
5*4*3*2 Mod 17 = 1
Now the remaining balances are 8*4*8*1
64 mod 17 = 13
13* 4 Mod 17= 1
Hence the Answer is 1

——————————————————————————

3)What is the remainder when difference of the 5th power
and the 4th power of 59 is divided by 11? ( 59^5-59^4)

59^5-59^4 mod 11
59^4( 59-1)
= 58*59^4
58 mod 11= 3
59 mod 11= 4
so we are left with 3*4^4 which is equal to 3*(4^2)^2
4^2 mod 11= 5
so we are left with 3*5*5 =75
75 mod 11= 9

———————————————————–

4)At what time after 4.00 p.m. is the minutes hand of a clock exactly aligned with the hour hand?

Answer

4:21:49.5

Assume that X minutes after 4.00 PM minute hand exactly aligns with and hour hand.

For every minute, minute hand travels 6 degrees.
Hence, for X minutes it will travel 6 * X degrees.

For every minute, hour hand

travels 1/2 degrees.
Hence, for X minutes it will travel X/2 degrees.

At 4.00 PM, the angle between minute hand and hour hand is 120 degrees. Also, after X minutes, minute hand and hour hand are exactly aligned. So the angle with respect to 12 i.e. Vertical Plane will be same. Therefore,

6 * X = 120 + X/2
12 * X = 240 + X
11 * X = 240
X = 21.8182
X = 21 minutes 49.5 seconds

Hence, at 4:21:49.5 minute hand is exactly aligned with the hour hand.

———————————————————-

5)If a rook and a bishop of a standard chess set are randomly placed on a chessboard, what is the probability that one is attacking the other?

Note that both are different colored pieces.
SubmAnswer

The probability of either the Rook or the Bishop attacking the other is 0.3611

A Rook and a Bishop on a standard chess-board can be arranged in 64P2 = 64*63 = 4032 ways

Now, there are 2 cases – Rook attacking Bishop and Bishop attacking Rook. Note that the Rook and the Bishop never attack each other simultaneously. Let’s consider both the cases one by one.

Case I – Rook attacking Bishop
The Rook can be placed in any of the given 64 positions and it always attacks 14 positions. Hence, total possible ways of the Rook attacking the Bishop = 64*14 = 896 ways

Case II – Bishop attacking Rook
View the chess-board as a 4 co-centric hollow squares with the outermost square with side 8 units and the innermost square with side 2 units.

If the bishop is in one of the outer 28 squares, then it can attack 7 positions. If the bishop is in one of the 20 squares at next inner-level, then it can attack 9 positions. Similarly if the bishop is in one of the 12 squares at next inner-level, then it can attack 11 positions. And if the bishop is in one of the 4 squares at next inner-level (the innermost level), then it can attack 13 positions.

Hence, total possible ways of the Bishop attacking the Rook
= 28*7 + 20*9 + 12*11 + 4*13
= 560 ways

Thus, the required probability is
= (896 + 560) / 4032
= 13/36
= 0.3611

Posted by: SATYASRINIVAS | June 4, 2007

formulae11

Apollonius theorem ; In a triangle ABC , if AD
is the median to the side BC , then
AB^2 + AC^2 = 2(AD^2 + BD^2) or 2(AD^2 + DC^2) .
Note BD=DC=BC/2.

—————————————————————————————-

Let the sides be A,B,C.

Semiperimeter = (A+B+C)/2

Area =(S*(S-A)*(S-B)*(S-C))^0.5

Inradius = Area/ Semiperimeter

Circumradius= A.B.C/ 4.Area

—————————————————————————————–

if n is number of sides.
For any regular polynomial, each angle =((n-2)*180)/n and
Total sum of the angles = (n-2)*180 or Each angle* n

——————————————————————————

Wrong Weight*(100 + Profit %)/100 = Correct Weight

———————————————————————————-

1. 1st January 0001 and every 400 years after that is a Monday.
That is 1st Jan of year 0001, 401, 801,1201,1601,2001 is
Monday.
2. An year divisible by 4 is a leap year, but century years are not
leap years unless they are divisible by 400. So 2000 is a Leap
Year but 1900, 1800, 1700 are not not leap year.
3. Odd days is the remainder obtained when the number of days
is divided by 7. Example: If it is Sunday today , after 50 days it will
be: 50/7 gives remained 1. Add 1 day to Sunday to get answer
as Monday.
4. A non leap year has 1 odd day and a leap year has 2 odd
days.
5. A normal Century has 5 odd days and leap century has 6 odd
days.
6. January, March, May, July, Aug, Oct and December have 3 odd
days each. April, June, Sept and Nov have 2 odd days each. Feb
has 0 odd days if it is not a leap year and has 1 odd day if it is a
leap year.
6. Number of leap years between any two given years is equal to
the quotient when the difference between the two given years is
divided by 4. Example Number of Leap years between 1947 to
1901 = 1947-1901= 46. 46 /4 = 11.5. So number of leap years=11.

 

What was the day on 15 Aug 1947 ?

Odd year for 1601-1900 : 5+5+5=15 or 1 odd day
1947-1901= 46. No of odd days =46 or 4
Number of leap years = 46/4=11. No. of odd days =11 or 4
Odd days till July end : 3+0+3+2+3+2+3= 16 or 2
Day is August = 15 or 1
Total Odd days =1+4+4+2+1= 12 or 5 odd days.
So 15th Aug 1947 was Friday.

——————————————————————–

Arithmetic series

Sn= n(2a +(n-1)d) / 2
Tn= a + (n-1)d

A.M*HM=GM^2

geometric progression

Tn=ar^(n-1)

Sn= a[ (1-r^n)/ (1-r) ] where r<1

Sn= a[ (r^n-1)/ (r-1) ] where r>1

S(infinity)= a/ (1-r) when r<1

——————————————————————

Right angle triangle:The square of the shortest side is less than the product of the
sum and the difference of the longest and the third side.

Posted by: SATYASRINIVAS | May 31, 2007

quntspoint to remember

COMMON ADMISSION TEST – MBA ENTRANCE

Quantitative Ability – POINTS TO REMEMBER

  1. If an equation (i.e. f(x) = 0) contains all positive co-efficients of any powers of x, it has no positive roots.

Eg: x3+3x2+2x+6=0 has no positive roots

  1. For an equation, if all the even powers of x have same sign coefficients and all the odd powers of x have the opposite sign coefficients, then it has no negative roots.

  1. For an equation f(x)=0 , the maximum number of positive roots it can have is the number of sign changes in f(x) ; and the maximum number of negative roots it can have is the number of sign changes in f(-x)

  1. Complex roots occur in pairs, hence if one of the roots of an equation is 2+3i, another has to be 2-3i and if there are three possible roots of the equation, we can conclude that the last root is real. This real root could be found out by finding the sum of the roots of the equation and subtracting (2+3i)+(2-3i)=4 from that sum.

ü For a cubic equation ax3+bx2+cx+d=o

    • Sum of the roots = – b/a
    • Sum of the product of the roots taken two at a time = c/a
    • Product of the roots = -d/a

ü For a bi-quadratic equation ax4+bx3+cx2+dx+e = 0

    • Sum of the roots = – b/a
    • Sum of the product of the roots taken three at a time = c/a
    • Sum of the product of the roots taken two at a time = -d/a
    • Product of the roots = e/a

  1. If an equation f(x)= 0 has only odd powers of x and all these have the same sign coefficients or if f(x) = 0 has only odd powers of x and all these have the same sign coefficients, then the equation has no real roots in each case (except for x=0 in the second case)

  1. Consider the two equations

a1x+b1y=c1

a2x+b2y=c2

Then,

ü If a1/a2 = b1/b2 = c1/c2, then we have infinite solutions for these equations.

ü If a1/a2 = b1/b2 <> c1/c2, then we have no solution.

ü If a1/a2 <> b1/b2, then we have a unique solution.

  1. Roots of x2 + x + 1=0 are 1, w, w2 where 1 + w + w2=0 and w3=1

  1. |a| + |b| = |a + b| if a*b>=0

else, |a| + |b| >= |a + b|

  1. The equation ax2+bx+c=0 will have max. value when a<0 and min. value when a>0. The max. or min. value is given by (4ac-b2)/4a and will occur at x = -b/2a

ü If for two numbers x + y=k (a constant), then their PRODUCT is MAXIMUM if x=y (=k/2). The maximum product is then (k2)/4.

ü If for two numbers x*y=k (a constant), then their SUM is MINIMUM if
x=y (=root(k)). The minimum sum is then 2*root (k).

  1. Product of any two numbers = Product of their HCF and LCM. Hence product of two numbers = LCM of the numbers if they are prime to each other.

  1. For any 2 numbers a, b where a>b

ü a>AM>GM>HM>b (where AM, GM ,HM stand for arithmetic, geometric , harmonic means respectively)

ü (GM)^2 = AM * HM

  1. For three positive numbers a, b, c

ü (a + b + c) * (1/a + 1/b + 1/c)>=9

  1. For any positive integer n

ü 2<= (1 + 1/n)^n <=3

  1. a2 + b2 + c2 >= ab + bc + ca

If a=b=c, then the case of equality holds good.

  1. a4 + b4 + c4 + d4 >= 4abcd (Equality arises when a=b=c=d=1)

  1. (n!)2 > nn

  1. If a + b + c + d=constant, then the product a^p * b^q * c^r * d^s will be maximum if a/p = b/q = c/r = d/s

  1. If n is even, n(n+1)(n+2) is divisible by 24

  1. x^n -a^n = (x-a)(x^(n-1) + x^(n-2) + …….+ a^(n-1) ) ……Very useful for finding multiples. For example (17-14=3 will be a multiple of 17^3 – 14^3)

  1. e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ……..to infinity

Note: 2 < e < 3

  1. log(1+x) = x – (x^2)/2 + (x^3)/3 – (x^4)/4 ………to infinity [Note the alternating sign . .Also note that the logarithm is with respect to base e]

  1. (m + n)! is divisible by m! * n!

  1. When a three digit number is reversed and the difference of these two numbers is taken, the middle number is always 9 and the sum of the other two numbers is always 9.

  1. Any function of the type y=f(x)=(ax-b)/(bx-a) is always of the form x=f(y)

  1. To Find Square of a 3-Digit Number

Let the number be XYZ

Step No.

Operation to be Performed

1

Last digit = Last digit of Sq(Z)

2

Second last digit = 2*Y*Z + any carryover from STEP 1

3

Third last digit 2*X*Z+ Sq(Y) + any carryover from STEP 2

4

Fourth last digit is 2*X*Y + any carryover from STEP 3

5

Beginning of result will be Sq(X) + any carryover from Step 4

Eg) Let us find the square of 431

Step No.

Operation to be Performed

1

Last digit = Last digit of Sq(1) = 1

2

Second last digit = 2*3*1 + any carryover from STEP 1=6+0=6

3

Third last digit 2*4*1+ Sq(3) + any carryover from STEP 2 = 8+9+0 = 17 i.e. 7 with carry over of 1

4

Fourth last digit is 2*4*3 + any carryover from STEP 3 = 24+1 = 25 i.e. 5 with carry over of 2

5

Beginning of result will be Sq(4) + any carryover from Step 4 = 16+2 = 18

THUS SQ(431) = 185761

If the answer choices provided are such that the last two digits are different, then, we need to carry out only the first two steps only.

ü The sum of first n natural numbers = n(n+1)/2

ü The sum of squares of first n natural numbers is n(n+1)(2n+1)/6

ü The sum of cubes of first n natural numbers is (n(n+1)/2)2/4

ü The sum of first n even numbers= n (n+1)

ü The sum of first n odd numbers= n2

  1. If a number ‘N’ is represented as a^x * b^y * c^z… where {a, b, c, …} are prime numbers, then

ü the total number of factors is (x+1)(y+1)(z+1) ….

ü the total number of relatively prime numbers less than the number is
N * (1-1/a) * (1-1/b) * (1-1/c)….

ü the sum of relatively prime numbers less than the number is
N/2 * N * (1-1/a) * (1-1/b) * (1-1/c)….

ü the sum of factors of the number is {a^(x+1)} * {b^(y+1)} * …../(x * y *…)

ü Total no. of prime numbers between 1 and 50 is 15

ü Total no. of prime numbers between 51 and 100 is 10

ü Total no. of prime numbers between 101 and 200 is 21

ü The number of squares in n*m board is given by m*(m+1)*(3n-m+1)/6

ü The number of rectangles in n*m board is given by n+1C2 * m+1C2

  1. If ‘r’ is a rational no. lying between 0 and 1, then, r^r can never be rational.

  1. Certain nos. to be remembered

ü 210 = 45 = 322 = 1024

ü 38 = 94 = 812 = 6561

ü 7 * 11 * 13 = 1001

ü 11 * 13 * 17 = 2431

ü 13 * 17 * 19 = 4199

ü 19 * 21 * 23 = 9177

ü 19 * 23 * 29 = 12673

  1. Where the digits of a no. are added and the resultant figure is 1 or 4 or 7 or 9, then, the no. could be a perfect square.

  1. If a no. ‘N’ has got k factors and a^l is one of the factors such that l>=k/2, then, a is the only prime factor for that no.

  1. To find out the sum of 3-digit nos. formed with a set of given digits

This is given by (sum of digits) * (no. of digits-1)! * 1111…1 (i.e. based on the no. of digits)

Eg) Find the sum of all 3-digit nos. formed using the digits 2, 3, 5, 7 & 8.

Sum = (2+3+5+7+8) * (5-1)! * 11111 (since 5 digits are there)

= 25 * 24 * 11111

=6666600

  1. Consider the equation x^n + y^n = z^n

As per Fermat’s Last Theorem, the above equation will not have any solution whenever n>=3.

  1. Further as per Fermat, where ‘p’ is a prime no. and ‘N’ is co-prime to p, then,
    N^(p-1) – 1 is always divisible by p.

  1. 145 is the 3-digit no. expressed as sum of factorials of the individual digits i.e.

145 = 1! + 4! + 5!

ü Where a no. is of the form a^n – b^n, then,

· The no. is always divisible by a – b

· Further, the no. is divisible by a + b when n is even and not divisible by
a + b when n is odd

ü Where a no. is of the form a^n + b^n, then,

· The no. is usually not divisible by a – b

· However, the no. is divisible by a + b when n is odd and not divisible by
a + b when n is even

  1. The relationship between base 10 and base ‘e’ in log is given by
    log10N = 0.434 logeN

  1. WINE and WATER formula

Let Q – volume of a vessel, q – qty of a mixture of water and wine be removed each time from a mixture, n – number of times this operation is done and A – final qty of wine in the mixture, then,

A/Q = (1-q / Q)^n

  1. Pascal’s Triangle for computing Compound Interest (CI)

The traditional formula for computing CI is

CI = P*(1+R/100)^N – P

Using Pascal’s Triangle,

Number of Years (N)

——————-

1 1

2 1 2 1

3 1 3 3 1

4 1 4 6 4 1

1 …. …. … … ..1

Eg: P = 1000, R=10 %, and N=3 years. What is CI & Amount?

Step 1:

Amount after 3 years = 1 * 1000 + 3 * 100 + 3 * 10 + 1 * 1 = Rs.1331

The coefficients – 1,3,3,1 are lifted from the Pascal’s triangle above.

Step 2:

CI after 3 years = 3*100 + 3*10 + 3*1 = Rs.331 (leaving out first term in step 1)

If N =2, we would have had,

Amt = 1 * 1000 + 2 * 100 + 1 * 10 = Rs.1210

CI = 2 * 100 + 1* 10 = Rs.210

  1. Suppose the price of a product is first increased by X% and then decreased by Y% , then, the final change % in the price is given by:

Final Difference% = X – Y – XY/100

Eg) The price of a T.V set is increased by 40 % of the cost price and then is decreased by 25% of the new price. On selling, the profit made by the dealer was Rs.1000. At what price was the T.V sold?

Applying the formula,

Final difference% = 40 – 25 – (40*25/100) = 5 %.

So if 5 % = 1,000

Then, 100 % = 20,000.

Hence, C.P = 20,000

& S.P = 20,000+ 1000= 21,000

  1. Where the cost price of 2 articles is same and the mark up % is same, then, marked price and NOT cost price should be assumed as 100.

ü Where ‘P’ represents principal and ‘R’ represents the rate of interest, then, the difference between 2 years’ simple interest and compound interest is given by P * (R/100)2

ü The difference between 3 years’ simple interest and compound interest is given by (P * R2 *(300+R))/1003

ü If A can finish a work in X time and B can finish the same work in Y time then both of them together can finish that work in (X*Y)/ (X+Y) time.

ü If A can finish a work in X time and A & B together can finish the same work in S time then B can finish that work in (XS)/(X-S) time.

ü If A can finish a work in X time and B in Y time and C in Z time then all of them working together will finish the work in (XYZ)/ (XY +YZ +XZ) time

ü If A can finish a work in X time and B in Y time and A, B & C together in S time then

· C can finish that work alone in (XYS)/ (XY-SX-SY)

· B+C can finish in (SX)/(X-S); and

· A+C can finish in (SY)/(Y-S)

  1. In case ‘n’ faced die is thrown k times, then, probability of getting atleast one more than the previous throw = nC5/n5

ü When an unbiased coin is tossed odd no. (n) of times, then, the no. of heads can never be equal to the no. of tails i.e. P (no. of heads=no. of tails) = 0

ü When an unbiased coin is tossed even no. (2n) of times, then,
P (no. of heads=no. of tails) = 1-(2nCn/22n)

  1. Where there are ‘n’ items and ‘m’ out of such items should follow a pattern, then, the probability is given by 1/m!

Eg)1. Suppose there are 10 girls dancing one after the other. What is the probability of A dancing before B dancing before C?

Here n=10, m=3 (i.e. A, B, C)

Hence, P (A>B>C) = 1/3!

= 1/6

Eg)2. Consider the word ‘METHODS’. What is the probability that the letter ‘M’ comes before ‘S’ when all the letters of the given word are used for forming words, with or without meaning?

P (M>S) = 1/2!

= 1/2

  1. CALENDAR

ü Calendar repeats after every 400 years.

ü Leap year- it is always divisible by 4, but century years are not leap years unless they are divisible by 400.

ü Century has 5 odd days and leap century has 6 odd days.

ü In a normal year 1st January and 2nd July and 1st October fall on the same day. In a leap year 1st January 1st July and 30th September fall on the same day.

ü January 1, 1901 was a Tuesday.

52.

ü For any regular polygon, the sum of the exterior angles is equal to 360 degrees, hence measure of any external angle is equal to 360/n (where n is the number of sides)

ü For any regular polygon, the sum of interior angles =(n-2)*180 degrees

So measure of one angle is (n-2)/n *180

ü If any parallelogram can be inscribed in a circle, it must be a rectangle.

ü If a trapezium can be inscribed in a circle it must be an isosceles trapezium (i.e. oblique sides equal).

  1. For an isosceles trapezium, sum of a pair of opposite sides is equal in length to the sum of the other pair of opposite sides (i.e. AB+CD = AD+BC, taken in order)

ü For any quadrilateral whose diagonals intersect at right angles, the area of the quadrilateral is

0.5*d1*d2, where d1, d2 are the length of the diagonals.

ü For a cyclic quadrilateral, area = root((s-a) * (s-b) * (s-c) * (s-d)), where
s=(a + b + c + d)/2

Further, for a cyclic quadrilateral, the measure of an external angle is equal to the measure of the interior opposite angle.

ü Area of a Rhombus = Product of Diagonals/2

  1. Given the coordinates (a, b); (c, d); (e, f); (g, h) of a parallelogram , the coordinates of the meeting point of the diagonals can be found out by solving for

[(a + e)/2, (b + f)/2] = [(c + g)/2, (d + h)/2]

  1. Area of a triangle

ü 1/2*base*altitude

ü 1/2*a*b*sin C (or) 1/2*b*c*sin A (or) 1/2*c*a*sin B

ü root(s*(s-a)*(s-b)*(s-c)) where s=(a+b+c)/2

ü a*b*c/(4*R) where R is the circumradius of the triangle

ü r*s ,where r is the inradius of the triangle

  1. In any triangle

ü a=b*cos C + c*cos B

ü b=c*cos A + a*cos C

ü c=a*cos B + b*cos A

ü a/sin A=b/sin B=c/sin C=2R, where R is the circumradius

ü cos C = (a^2 + b^2 – c^2)/2ab

ü sin 2A = 2 sin A * cos A

ü cos 2A = cos^2 (A) – sin^2 (A)

  1. The ratio of the radii of the circumcircle and incircle of an equilateral triangle is 2:1

  1. Appollonius Theorem

In a triangle ABC, if AD is the median to side BC, then

AB2 + AC2 = 2(AD2 + BD2) or 2(AD2 + DC2)

ü In an isosceles triangle, the perpendicular from the vertex to the base or the angular bisector from vertex to base bisects the base.

ü In any triangle the angular bisector of an angle bisects the base in the ratio of the other two sides.

  1. The quadrilateral formed by joining the angular bisectors of another quadrilateral is always a rectangle.

  1. Let W be any point inside a rectangle ABCD, then,

WD2 + WB2 = WC2 + WA2

  1. Let a be the side of an equilateral triangle, then, if three circles are drawn inside this triangle such that they touch each other, then each circle’s radius is given by a/(2*(root(3)+1))

ü Distance between a point (x1, y1) and a line represented by the equation
ax + by + c=0 is given by |ax1+by1+c|/Sq(a2+b2)

ü Distance between 2 points (x1, y1) and (x2, y2) is given by
Sq((x1-x2)2+ (y1-y2)2)

  1. Where a rectangle is inscribed in an isosceles right angled triangle, then, the length of the rectangle is twice its breadth and the ratio of area of rectangle to area of triangle is 1:2.

references

pagalguy.com

esnips.com

—–>back to top

Posted by: SATYASRINIVAS | May 30, 2007

maths tips(1)

Hi people,

Wanted to share some shortcuts that would be helpful in quant as well as DI sections. The shortcuts have been compiled from various threads of PG itself.

Dunno whether this is the right thread for this purpose but well, let me post.

If any parallelogram can be inscribed in a circle , it must be a rectangle.

If a quadrilateral circumscribes a circle , the sum of a pair of opposite sides is equal to the sum of the other pair .

The ratio of the radii of the circumcircle and incircle of an equilateral triangle is 2:1 .

for similar cones , ratio of radii = ratio of their bases.

the quadrilateral formed by joining the angular bisectors of another f a quadrilateral is always a rectangle.

Let W be any point inside a rectangle ABCD .
Then
WD^2 + WB^2 = WC^2 + WA^2

Let a be the side of an equilateral triangle . then if three circles be drawn inside
this triangle touching each other then each’s radius = a/(2*(root(3)+1))

Area of a regular hexagon : root(3)*3/2*(side)*(side)

the area of a regular n-sided polygon of side ‘a’ is given by
area=(n/4)*a^2*cot(180/n)

In any triangle
a=b*CosC + c*CosB
b=c*CosA + a*CosC
c=a*CosB + b*CosA
————————————————————

————————————————————
If a+b+c+d=constant , then the product a^p * b^q * c^r * d^s will be maximum
if a/p = b/q = c/r = d/s .
————————————————————
e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ……..to infinity
————————————————————
(m+n)! is divisible by m! * n!
————————————————————
for squares of numbers between 25 and 50.
let the number be 25+k
first calculate (25-k)^2 and to it add k*100
2)for squares of numbers between 50 and 75.
again let the number 50+k
calculate k^2 and to it add 2500+100*k
————————————————————
3)for squares of numbers between 75 and 100
let the number be 100-k
calculate k^2 and to it add (100-2*k)*100
these formulas are basically a derivation from the formulas (a+b)^2 and (a-b)^2.
————————————————————
2^2n -1 is always divisible by 3
2^2n -1 = (3-1)^2n -1
= 3M +1 -1
= 3M, thus divisible by 3
———————————-
if a number ‘n’ is represented as
n=a^x * b^y * c^z ….
where, {a,b,c,.. } are prime numbers then
Quote:
(a) the total number of factors is (x+1)(y+1)(z+1) ….
(b) the total number of relatively prime numbers less than the number is n * (1-1/a) * (1-1/b) * (1-1/c)…. ???????????????????
(c) the sum of relatively prime numbers less than the number is n/2 * n * (1-1/a) * (1-1/b) * (1-1/c)….
(d) the sum of factors of the number is {a^(x+1)} * {b^(y+1)} * …../(x*y*…)
—————————————–
what is the highest power of 10 in 203!ANS : express 10 as product of primes; 10 = 2*5
divide 203 with 2 and 5 individually
203/2 = 101
101/2 = 50
50/2 = 25
25/2 = 12
12/2 = 6
6/2 = 3
3/2 = 1
thus power of 2 in 203! is, 101 + 50 + 25 + 12 + 6 + 3 + 1 = 198
divide 203 with 5
203/5 = 40
40/5 = 8
8/5 = 1
thus power of 5 in 203! is, 49
so the power of 10 in 203! factorial is 49
——————————————————
n how many ways, 729 can be expressed as a difference of 2 squares?
ANS: 729 = a^2 – b^2
= (a-b)(a+b),
since 729 = 3^5,
total ways of getting 729 are, 1*729, 3*243, 9*81, 27*27.
So 4 ways
Funda is that, all four ways of expressing can be used to findout distinct a,b values,
for example take 9*81
now since 9*81 = (a-b)(a+b) by solving the system a-b = 9 and a+b = 81 we can have 45,36 as soln.
————————————–
if x%a=y%a = r then
(x-y)%r =0 (% stands for modulo operator)
———————————————
total number of primes between 1 and 100 – 25
———————————————-
Reminder Funda
(a) (a + b + c) % n = (a%n + b%n + c%n) %n
EXAMPLE: The reminders when 3 numbers 1221, 1331, 1441 are divided by certain number 9 are 6, 8, 1 respectively. What would be the reminder when you divide 3993 with
9? ( never seen such question though )
the reminder would be (6 + 8 + 1) % 9 = 6
————————————————–
(a*b*c) % n = (a%n * b%n * c%n) %n
————————————–
when a number is divided by 11,7,4 the reminders are 5,6,3 respectively. what would be the reminders when the same number is divided by 4,7,11 respectively?
ANS : whenever such problem is given,
we need to write the numbers in top row and rems in the bottom row like this
11 7 4
| \ \
5 6 3
( coudnt express here properly )
now the number is of the form, LCM ( 11,7,4 ) + 11*(3*7 + 6) + 5
that is 302 + LCM(11,7,4) and thus the rems when the same number is divided by 4,7,11 respectively are,
302 mod 4 = 2
75 mod 7 = 5
10 mod 11 = 10

————————————————————
Plz tell me the answer to remainder when 2^156 / 13 .

2^156/13 = 2^(6*26)/13 (156 = 26 x 6)
= 64^26/13 = (65-1)^26/13 (since 65 is multiple of 13)
= (-1)^26=1
u just have to bring close to the multiple of the number which divides the numerator..(like 65 in this case)…..
———————————————————–
In how many ways can 2310 be expressed as a product of 3 factors?
ANS: 2310 = 2*3*5*7*11
When a number can be expressed as a product of n distinct primes,
then it can be expressed as a product of 3 numbers in (3^(n-1) + 1)/2 ways
(I guess this is incorrect)
————————————————————-
Multiplication by 7: Going from right to left, we use
this rule: Double each number and add half the
neighbor (digit to the right, dropping any fraction);
add 5 if the number (not the neighbor) is odd. And of
course, we have to deal with carries:
3852 x 7 = 26964
Starting at the right (2), we double the first number
(it has no neighbor) and write down the right-most
digit of that (4) and we have no carry. Then we double
the next number (2×5=10), add five (+5=15), and add
half the neighbor (+1=16), and write down the right
digit (6) of that and carry the 1. Then we double the
next number (2×8=16), and add half the neighbor
(+2=1, and add the carry (+1=19). Then we double the
next number (2×3=6), add five (+5=11), add half the
neighbor (+4=15), and add the carry (+1=16). Now we
double a zero off to the left of our 3852
(Trachtenberg wrote the zero out there: 03852) and add
half the neighbor (0+1=1), and add the carry (+1=2).
And we have our answer.
Notice that the carries are smaller than they were in
normal multiplication by 7. The above rule is not
simple, but once mastered, it is easy to use. It
should be about as fast as multiplying normally (which
requires memorizing the multiplication table).
Multiplication by other small numbers (3 through 12)
uses similar rules.
————————————-
Square 2-digit

Rule:
1. Square the second digit
2. Multiply the two digits and double
3. Square the first digit

example
49
81 L.D. 1 cy=8
4*9*2=72 +8 = 80 cy=8
4*4=16 + 8=24
ans=2401
——————————————-
Multiply just-under numbers

Example:
98
x 99
100 – 98 = 2 picture 98 2
100 – 99 = 1 picture 99 1
97 98 – 1 (upper left – lower right)
02 2 x 1 (multiply two right numbers)
9702
98 x 99 = 9702
99*94
99 1
94 6
(99-6)1*6=9306
————————————————————
Multiply just-over numbers

Example:
104
x106
104 -100 = 4 picture 104 4
106 -100 = 6 picture 106 6
110 104+6 (upper left + lower right)
24 4 x 6 (multiply two right numbers)
11024
104 x 106 = 11024
————————————————————–
Multiply just over and just under numbers
97*104
97 -3
104 4
101 -12
100 88 (subtract 1 from the result of cross addition. take the complement of the right multiplication)
10088
103*96
103 3
96 -4
99 -12
9888
————————————————————
38*32=1216.ie,3*4=12 and 8*2=16.only criteria is that the units digit number should add to 10 and that the ten’s digit number shud b the same
————————————————————
3)multiply 57 by 63
method :
5 7
| \ / |
| / \ |
6 3
__________
35 9 1
There are 3 steps:
a)Multiply vertically on the right: 7 x 3 = 21
This gives the last figure of the answer 1 and 2 as carry.
b) Multiply crosswise and add: (5 x 3 + 6 x 7) + 2(carry) = 59
This gives the middle figure 9 and 5 as carry.
c) Multiply vertically on the left: (5 x 6) + 5(carry) = 35.
This gives the first figure of the answer.

for 3 digits
127*93
12 7
9 3
118 1 1
——————————————————
Square just-under numbers

Example:
96^2
100 – 96 is 4
92 96 – 4 is 92
16 4 squared is 16
9216
962 = 9216
—————————————
Square just-over numbers

Example:
106^2
106 – 100 is 6
112 106 + 6
36 6^2
Ans: 11236
—————————————-
Square of number between 50 and 60
Example:
56^2
31 25 + last digit (25+6)
36 sqare of last digit (62)
3136
562 = 3136
———————–
Find remainder when 2222^5555 + 5555^2222 is divided by 7
2222 mod 7=3
5555 mod 7 = 4
so prob reduces to 3^5555 +4^2222 remainder 7
now this can b written as 243^1111 + 16^1111 remainder 7
now use direct formula tht x^n + y^n is divisible by x+y if n is odd
given expression is divisible by 243+16=259
so it is also divisible by 7
and hence remainder=0

anoter method:
Well fermat’s rule states that
a^(p-1) whenever divided by p where p is a prime no. and a is coprime to p, then the remainder would be 1.
as the divisor is 7 and both 2222 and 5555 are coprime to 7 thus any1 of them raised to the power of 6 or a multiple of it would give remainder as 1
2222^5555 + 5555^2222 is equivqlent to
3^5555 + 4^2222 which is
3^(6k+5) + 4^(6m+2)
which is 3^5 + 4^2 (since 3^6 and 4^6 will give 1 as remainder)
——————————————————–
Some pythagorean triplets:
3,4,5 (3^2=4+5)
5,12,13 (5^2=12+13)
7,24,25 (7^2=24+25)
8,15,17 (8^2 / 2 = 15+17 )
9,40,41 (9^2=40+41)
11,60,61 (11^2=60+61)
12,35,37 (12^2 / 2 = 35+37)
16,63,65 (16^2 /2 = 63+65)
20,21,29(EXCEPTION)
—————————————————-
For a set of fractions ( num<den), if the difference between the numerator and the denominator is the same, then the fraction with the largest numerator is the largest and the one with the smallest numerator is the smallest
e.g. 21/27, 23/29, 19/26
largest: 23/29
smallest: 19/26
———————————————————–
For a set of fractions ( num>den), if the difference between the numerator and the denominator is the same, then the fraction with the smallest numerator is the largest and the one with the largest numerator is the smallest
e.g. 27/21, 29/23, 26/19
smallest: 29/23
largest: 26/19
——————————————————————-
i guess we could find sqrt for numbers whose nearby sqrt we already know.
steps are :-
1. take the difference from the nearest smaller perfect square. for eg. sqrt (39) nearest perfect square is 36(whose sqrt we know as 6). and the difference is 39-36=3.
2. divide the difference with product of 2 and sq root of the number which we know.
ie difference 3/(2* sqrt(36) )
3/(2*6)=.25
3.sum the above with the sqrt which we know
ie .25+6=6.25
also works for subtraction
sqrt(33) = 6-.25 = 5.75 (aprox)
4. there is a great chance of getting the answer right with even the first decimal
is correct in most of the cases.

——————————————————————
Finding square root:
Splitting the difference:
Sqrt(3125) : group the digits taking two at a time from the left (like in the usual way of finding sq roots)
First pair: 31
1)We know 5*5 =25
2)rough estimate sqrt is 50
3)divide 3125by 50 =62.5
4)subtracton: 62.5-50 =12.5
5)divide 12.5 by 2 =6.25
round it off downwards :6
rough estimate 50+6=56

try this one:
sqrt(93560)
9,35,60
roughly :300
div 93560 by 300
311.8667-300=11.87
11.87/2=5.935
approx 6
ans 306
sqrt(3847214
38 47 21 48
approx 6000
38472148/6000
6412.014-6000=412.014
412.114/2=206.05
6206.05…(has considerable error)
In most cases error is just 1%
——————————————————————
————————————–
when a number is divided by 11,7,4 the reminders are 5,6,3 respectively. what would be the reminders when the same number is divided by 4,7,11 respectively?
ANS : whenever such problem is given,
we need to write the numbers in top row and rems in the bottom row like this
11 7 4
| \ \
5 6 3
( coudnt express here properly )
now the number is of the form, LCM ( 11,7,4 ) + 11*(3*7 + 6) + 5
that is 302 + LCM(11,7,4) and thus the rems when the same number is divided by 4,7,11 respectively are,
302 mod 4 = 2
75 mod 7 = 5
10 mod 11 = 10

————————————————————
Plz tell me the answer to remainder when 2^156 / 13 .

2^156/13 = 2^(6*26)/13 (156 = 26 x 6)
= 64^26/13 = (65-1)^26/13 (since 65 is multiple of 13)
= (-1)^26=1
u just have to bring close to the multiple of the number which divides the numerator..(like 65 in this case)…..
———————————————————–
In how many ways can 2310 be expressed as a product of 3 factors?
ANS: 2310 = 2*3*5*7*11
When a number can be expressed as a product of n distinct primes,
then it can be expressed as a product of 3 numbers in (3^(n-1) + 1)/2 ways
(I guess this is incorrect)
————————————————————-
Multiplication by 7: Going from right to left, we use
this rule: Double each number and add half the
neighbor (digit to the right, dropping any fraction);
add 5 if the number (not the neighbor) is odd. And of
course, we have to deal with carries:
3852 x 7 = 26964
Starting at the right (2), we double the first number
(it has no neighbor) and write down the right-most
digit of that (4) and we have no carry. Then we double
the next number (2×5=10), add five (+5=15), and add
half the neighbor (+1=16), and write down the right
digit (6) of that and carry the 1. Then we double the
next number (2×8=16), and add half the neighbor
(+2=1, and add the carry (+1=19). Then we double the
next number (2×3=6), add five (+5=11), add half the
neighbor (+4=15), and add the carry (+1=16). Now we
double a zero off to the left of our 3852
(Trachtenberg wrote the zero out there: 03852) and add
half the neighbor (0+1=1), and add the carry (+1=2).
And we have our answer.
Notice that the carries are smaller than they were in
normal multiplication by 7. The above rule is not
simple, but once mastered, it is easy to use. It
should be about as fast as multiplying normally (which
requires memorizing the multiplication table).
Multiplication by other small numbers (3 through 12)
uses similar rules.
————————————-
Square 2-digit

Rule:
1. Square the second digit
2. Multiply the two digits and double
3. Square the first digit

example
49
81 L.D. 1 cy=8
4*9*2=72 +8 = 80 cy=8
4*4=16 + 8=24
ans=2401
——————————————-
Multiply just-under numbers

Example:
98
x 99
100 – 98 = 2 picture 98 2
100 – 99 = 1 picture 99 1
97 98 – 1 (upper left – lower right)
02 2 x 1 (multiply two right numbers)
9702
98 x 99 = 9702
99*94
99 1
94 6
(99-6)1*6=9306
————————————————————
Multiply just-over numbers

Example:
104
x106
104 -100 = 4 picture 104 4
106 -100 = 6 picture 106 6
110 104+6 (upper left + lower right)
24 4 x 6 (multiply two right numbers)
11024
104 x 106 = 11024
————————————————————–
Multiply just over and just under numbers
97*104
97 -3
104 4
101 -12
100 88 (subtract 1 from the result of cross addition. take the complement of the right multiplication)
10088
103*96
103 3
96 -4
99 -12
9888
————————————————————
38*32=1216.ie,3*4=12 and 8*2=16.only criteria is that the units digit number should add to 10 and that the ten’s digit number shud b the same
————————————————————
3)multiply 57 by 63
method :
5 7
| \ / |
| / \ |
6 3
__________
35 9 1
There are 3 steps:
a)Multiply vertically on the right: 7 x 3 = 21
This gives the last figure of the answer 1 and 2 as carry.
b) Multiply crosswise and add: (5 x 3 + 6 x 7) + 2(carry) = 59
This gives the middle figure 9 and 5 as carry.
c) Multiply vertically on the left: (5 x 6) + 5(carry) = 35.
This gives the first figure of the answer.

for 3 digits
127*93
12 7
9 3
118 1 1
——————————————————
Square just-under numbers

Example:
96^2
100 – 96 is 4
92 96 – 4 is 92
16 4 squared is 16
9216
962 = 9216
—————————————
Square just-over numbers

Example:
106^2
106 – 100 is 6
112 106 + 6
36 6^2
Ans: 11236
—————————————-
Square of number between 50 and 60
Example:
56^2
31 25 + last digit (25+6)
36 sqare of last digit (62)
3136
562 = 3136
———————–
Find remainder when 2222^5555 + 5555^2222 is divided by 7
2222 mod 7=3
5555 mod 7 = 4
so prob reduces to 3^5555 +4^2222 remainder 7
now this can b written as 243^1111 + 16^1111 remainder 7
now use direct formula tht x^n + y^n is divisible by x+y if n is odd
given expression is divisible by 243+16=259
so it is also divisible by 7
and hence remainder=0

anoter method:
Well fermat’s rule states that
a^(p-1) whenever divided by p where p is a prime no. and a is coprime to p, then the remainder would be 1.
as the divisor is 7 and both 2222 and 5555 are coprime to 7 thus any1 of them raised to the power of 6 or a multiple of it would give remainder as 1
2222^5555 + 5555^2222 is equivqlent to
3^5555 + 4^2222 which is
3^(6k+5) + 4^(6m+2)
which is 3^5 + 4^2 (since 3^6 and 4^6 will give 1 as remainder)
——————————————————–
Some pythagorean triplets:
3,4,5 (3^2=4+5)
5,12,13 (5^2=12+13)
7,24,25 (7^2=24+25)
8,15,17 (8^2 / 2 = 15+17 )
9,40,41 (9^2=40+41)
11,60,61 (11^2=60+61)
12,35,37 (12^2 / 2 = 35+37)
16,63,65 (16^2 /2 = 63+65)
20,21,29(EXCEPTION)
—————————————————-
For a set of fractions ( num<den), if the difference between the numerator and the denominator is the same, then the fraction with the largest numerator is the largest and the one with the smallest numerator is the smallest
e.g. 21/27, 23/29, 19/26
largest: 23/29
smallest: 19/26
———————————————————–
For a set of fractions ( num>den), if the difference between the numerator and the denominator is the same, then the fraction with the smallest numerator is the largest and the one with the largest numerator is the smallest
e.g. 27/21, 29/23, 26/19
smallest: 29/23
largest: 26/19
——————————————————————-
i guess we could find sqrt for numbers whose nearby sqrt we already know.
steps are :-
1. take the difference from the nearest smaller perfect square. for eg. sqrt (39) nearest perfect square is 36(whose sqrt we know as 6). and the difference is 39-36=3.
2. divide the difference with product of 2 and sq root of the number which we know.
ie difference 3/(2* sqrt(36) )
3/(2*6)=.25
3.sum the above with the sqrt which we know
ie .25+6=6.25
also works for subtraction
sqrt(33) = 6-.25 = 5.75 (aprox)
4. there is a great chance of getting the answer right with even the first decimal
is correct in most of the cases.

——————————————————————
Finding square root:
Splitting the difference:
Sqrt(3125) : group the digits taking two at a time from the left (like in the usual way of finding sq roots)
First pair: 31
1)We know 5*5 =25
2)rough estimate sqrt is 50
3)divide 3125by 50 =62.5
4)subtracton: 62.5-50 =12.5
5)divide 12.5 by 2 =6.25
round it off downwards :6
rough estimate 50+6=56

try this one:
sqrt(93560)
9,35,60
roughly :300
div 93560 by 300
311.8667-300=11.87
11.87/2=5.935
approx 6
ans 306
sqrt(3847214
38 47 21 48
approx 6000
38472148/6000
6412.014-6000=412.014
412.114/2=206.05
6206.05…(has considerable error)
In most cases error is just 1%
——————————————————————
——————————————
We all know the traditional formula to compute interest…
CI = P*(1+R/100)^N – P
The calculation get very tedious when N>2 (more than 2 years). The method suggested below is elegant way to get CI/Amount after ‘N’ years.
You need to recall the good ol’ Pascal’s Triange in following way:
Code:

Number of Years (N)
——————-
1 1
2 1 2 1
3 1 3 3 1
4 1 4 6 4 1
. 1 …. …. … … 1

Example: P = 1000, R=10 %, and N=3 years. What is CI & Amount?
Step 1: 10% of 1000 = 100, Again 10% of 100 = 10 and 10% of 10 = 1
We did this three times b’cos N=3.
Step 2:
Now Amount after 3 years = 1 * 1000 + 3 * 100 + 3 * 10 + 1 * 1 = Rs.1331/-
The coefficents – 1,3,3,1 are lifted from the pascal’s triangle above.
Step 3:
CI after 3 years = 3*100 + 3*10 + 3*1 = Rs.331/- (leaving out first term in step 2)
If N =2, we would have had, Amt = 1 * 1000 + 2 * 100 + 1 * 10 = Rs. 1210/-
CI = 2 * 100 + 1* 10 = Rs. 210/-
This method is extendable for any ‘N’ and it avoids calculations involving higher powers on ‘N’ altogether!
A variant to this short cut can be applied to find depreciating value of some property. (Example, A property worth 100,000 depreciates by 10% every year, find its value after ‘N’ years).
Pascal’s triangle works in all cases but the problem being that it’s lot easier if P(Principal) and R(Rate of interest) are multiples of 10.The problem arises when either the principal or rate of interest or both are not multiples of 10.The calculation becomes a li’l bit complicated …or at least that’s what i think…in the example below R is not 10 and still it works…
For example:P=700,R=8%,N=3
(8/100)*700=56
(8/100)*56=4.48
(8/100)*4.48=0.3584
So CI=(1*700+3*56+3*4.48+1*0.3584)-700=181.7984
and if you would hav calculated in the original method
C.I=700(1+8/100)^3 – 700=700(1.08*1.08*1.0-700=181.7984
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When interest is calculated as CI, the number of years for the Amount to double (two times the principal) can be found with this following formula:
R * N ~ 72 (approximately equal to).
Exampe, if R=6% p.a. then it takes roughly 12 years for the Principal to double itself.
Note: This is just a approximate formula (when R takes large values, the error % in formula increases).
When interest is calculated as SI, number of years for amt to double can be found as:
N * R = 100 . BTW this formula is exact!

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Let’s say we want to find 14.25% of 3267.
What will 10% of 3267 be… 326.7
And 1%… obviously 32.67. Then what would 4% be… 128 for 32 and 2.68 for 0.67…, i.e. 130.6
Thus, 14% will be 326.7 + 130.6, i.e. 457.3
If I want an even more accurate answer, if 1% is 32.6, then 0.25% will be 1/4 of 32.6, i.e 8.15
14.25% of 3267 will be 465.4
Knowing reciprocal percentage equivalent, I should have thought of an even better factorisation as 14.28% – 0.03% and since 14.28% is nothing but 1/7, the answer can directly be found by dividing 3267 by 7, i.e. 466.7

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a% of b = b% of a
so, sometimes if 4% of 25 is to be found, finding 25% of 4 would be a more sensible way
—————————————————

Percentage Table

SUBTRACTED ADDED
4 4.16(1/24) 3.86(1/26)
5 5.26(1/19) 4.76(1/21)
10 11.11(1/9) 9.09(1/11)
12.5 14.28(1/7) 11.11(1/9)
15 17.55 13
20 25 16.67(1/6)
25 33.33 20(1/5)
30 42.8 23
40 66.67(2/3) 28
50 100 33.33(1/3)
60 150 37.5(3/
when subtracted then add this% when added the subtarct this%

neha’s table of percentages.
first its uses: the info is xtremely important when dealing with problems of type..
say price increased by x% how much shud consumption decrease so that expenditure remains same.
also since most of the time speed dist..problems are in the end ratio proportion kind
this info will be xtremely useful..
so the info given is if increase is 25% decrease reqd to negate it is 20%.
In fact the table need not be memorized.the whole work can be done mentally without much problem..
the trick is to use 100 as a base and work on it..
for eg ..imagine price and consumption both as 100
now price increases by 25%..therefore ratio of new price/old price = 125/100
=> ratio of new consumption/old consumption = inverse of prev ratio = 100/125
=>change (decrease)= (125-100)/125 = 25/125= 20%
ive unnecessarily gone to such detail with the calc ..with xperience this is very simple..
for eg: 4% decrease
here’s how one shud work it out.
4% decrease =>96/100 invert it=>100/96=>change 4/96 = > 1/24
this is as given in the table.
nother one 5% increase => 105/100=>100/105=>5/105=>1/21

————————————————-

Problem : 2485/179379 = ?
1. Take the denominator(179379)
2. See what percentage would give you same no of digits as numerator. In this case 1% of 179379 = 1793.79.
3. Now you need another~ 600 to get to 2400 which is 30% (.3% w.r.t original denominator) of 1793.79 ~ 1800.
4. This gives us all together 1.3% of denominator or .013 as quotient.

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The sum of terms from x to y where x and y are non negative intergers and y > x is
(sqr(y) – sqr(x) + x + y )/2

d/dx of (x+a)(x+b)(x+c)(x+d) = (x+b)(x+c)(x+d)d/dx(x+a) + (x+a)(x+c)(x+d)d/dx(x+b) + (x+b)(x+a)(x+d)d/dx(x+c) + (x+b)(x+c)(x+a)d/dx(x+d)

Cheers

VIVEK

references

pagalguy.com

esnips.com

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