Algebra

1) 1. A pharmacist has 8 liters of a 15 percent solution of acid. How

much distilled water must she add to reduce the concentration of acid

to 10 percent?

2. By installing a $120 thermostat that reduces the temperature

setting at night, a family hopes to cut its annual bill for heating

oil by 8 percent, and thereby recover the cost of the thermostat in

fuel savings after 2 years. What was the family’s annual fuel bill

before installing the thermostat?

2) Jay tiled a 15 feet by 21 feet rectangular ballroom with one-foot-

square tiles. When he finished, he drew both diagonals

connecting opposite corners of the room. What is the total number

of tiles that the diagonals passed through?

3) A man is walking across a railroad bridge that goes from point A

to point B. He starts at point A, and when he is 3/8 of the way

across the bridge, he hears a train approaching. The train’s speed

is 60 mph (miles per hour).

The man can run fast enough so that if he turns and runs back

toward point A, he will meet the train at A, and if he runs

forward toward point B, the train will overtake him at B.

How fast can the man run?

4)

If a+b+c=3 and

a(^2)+b(^2)+c(^2)=5 and

a(^3)+b(^3)+c(^3)=7

what is a(^4)+b(^4)+c(^4) ?

5)

A woman is walking down a downward-moving escalator and steps down 10

steps to reach the bottom. Just as she reaches the bottom of the

escalator, a sale commences on the floor above. She runs back up the

downward moving escalator at a speed five times that which she walked

down. She covers 25 steps in reaching the top. How many steps are

visible on the escalator when it is switched off?

6) On a string of 33 pearls, the middle pearl is the largest and most

expensive of all. Starting from one end, each pearl is worth $100 more

than the one before, up to the middle. From the other end, each pearl

is worth $150 more than the one before, up to the middle. The string

of pearls is worth $65,000. What is the value of the middle pearl?

7) smallest number with 24 distinct different positive factors

SET 1

1) A train leaves Patna at 5 am and reaches Delhi at 9 am. Another train

leaves Delhi at 6.30 am and reaches Patna at 10 am. At what time do the two

trains meet? (Ans. 7.40 am)

2) A man covers a certain distance on scooter. Had he moved 3 km/hr faster,

he would have taken 40 minuters less. If he had moved 2 km/hr slower, he

would have taken 40 minutes more. Find the distance in km and original speed

(Ans 40 km and 12 km/hr)

3)At what distance from Delhi will a train, which leaves Delhi for Amritsar

at 2.45 pm and goes at a rate of 50 km/hr, meet a train which leaves

Amritsar for Delhi at 1.35 pm and goes at the rate of 60 km/hr, the distance

between the towns being 510 km?

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SET 2

1.What is the sum of all the three digit numbers which leave the

remainder 1 when divided bby 4?

(a)123525 (b)122976 (c)112996 (d)100000

2.Ram, not so efficient technician, makes a bacteria culture using 5

E.Coli bacteria.Each e.coli bacteria divides into 2 every 10 mins.

After haf an hr, Ram by mistake introduces a culture of C.Coli

bacteria which had N bacteria. Each c.coli bacteria digests 2 e.coli

bacteria within 10 mins and then instantaneously divides into 2. If

an e.cloli bacteria is being digested, it cannot divide further.If at

the end of 60 mins from the begining, 32 e.coli bacteria were left,

how many c.coli bacteria had Ram introduced??

(a)6 (b)4 (c)8 (d)none

3.If Ram can slove 3 out of 10 prblems correctly on the average and

Mohan has an average of 7 out of 10, then how many problems out of 10

can be approx expected to be solved if both try to solve them togther?

(a)8 (b)9 (c)10 (d)cannot b determined

4.The sum of the mean and the mean of the reciprocals of 2 numbers is

(4509/200).The sum of the product of their reciprocals and their

product is (250001/500). Which of the following can be the larger

number?

(a)40 (b)20 (c)25 (d)50

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SET 3

1. A recurring deposit of Rs200 per month for 5 years would be

equivalent to a singledeposit of Rs 18300 in how many years??

(a) 2 years (b) 1year 8 months (c)3 years 6 months (d) 5 years

2.A reduction of 16 2/3% in the price of lemons enables a householder

to get 54 lemons more for Rs.81. What is the reduced price per lemon?

(a)60paise (b)50 paise (c)30 paise (d)25 paise

3.Five persons entered the lift cabin on the ground floor of an eight-

storey building. Suppose each of them, independently and with equal

probability, can leave the cabin at any floor beginning withe

first.Find the probablity of all the five persons leaving

at different floors.

(a)360/8^5 (b)360/6^5 (c)2520/7^5 (d)none of these

4.A man takes a step forward with 0.4 probability and backward with

probability 0.6. Find the probability that at the end of five steps

he is one step away from the starting point.

(a) 0.55 (b)0.56 (c)0.57 (d)0.6

5.Let Tn denote the number of triangles which can be formed using the

vertices of a regualr polygon of n sides.If Tn+1 – Tn =21, then n

equals

(a)5 (b)7 (c)6 (d) 4

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SET 4

1)Find the number of zeros in the product of

1^1 * 2^2 * 3^3*………*98^98*99^99*100^100

2)Remainder obtained when

43^101 + 23 ^101 is divided by 66

3)Last two digit of multiplication:

122*123*125*127*129

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SET 5

Q.1) 25^24/601, what is the remainder?

Q.2) 32^32^32/17, what is the remainder?

Q.3) What is the smallest integer which should be multiplied to 0.ababababab…….to make it an integer where a & b are any natural numbers?

Q.4) Find total factors for 32^3 – 60^3 + 28^3 ?

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SET 6

Q1)In a particular country where monogamy was a law ,3/5 of men were married to 2/3 of women What fraction of adult population was married ?

Options: A)7/19 B) 12/19 C)7/15 4)8/15

Q2)How many positive integers less than 100 and excluding 1 are coprimes of both 6 and 7?

Options: A)25 B)26 C)27 D)28 ( Answer is option C)

Q3)Ghosh babu estimated that he needed to plow 50 acres a day in order to be ready for Rabi planting. After plowing exactly half the land at that average rate ,he realised that he should have been plowing at a rate of 60 acres per day to meet the deadline?How many acres each day will he need to average in order to meet deadline?

Options:A)65 B)70 C)75 D)80

(Answer is Option C)

Q4)What is the remainder when 337,500,000 is divided by 128?

Options:A)0 B)32 C)64 D)96 (Answer is Option D)

Q5)The 4-digit number 6A6B is divisible by 72 ?What is the sum of the possible values of A?

Options :A)2 B)7 C)9 D)None (Ans is Option C)

Q6)A positive integer of 22 digits ,with the units digit as 7 is multiplied by 7?The resulting number also has 22 digits with shifting of the digit 7from extreme right to extreme left and with remaining digits in same order as before ?Find Sum of digits of the Number ?

Options A)37 B)59 C)85 D)96(Answer is Option D)

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SET 7

Q.1

For the same budgeted amount, Ramu could buy fewer oranges than before after 20% hike in the price of oranges. What is the minimum number of oranges that he bought originally, if after the hike he still managed to buy an integral number of oranges?

Q2.

There are four numbers in a sequence. The average of first three is 6, the average of the last three is 7, and the last number is 3 more than the first. What is the avg. of 2nd & 3rd number?

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SET 8

1)..In a four digit no. the sum of the first two digits is same as the next two digits. Sum of the first & the last digit is equal to the third digit. And finally sum of the second & the fourth digit is double than that of the first & the third digit. Which wil be the third digit of the four digit no?

1.1 2.4 3.5 4.8

2).. Sometimes after 10.00PM a murder took place.A witness claimed that the clock must have stopped at time of shooting .it was later found that the position of both the hands were same but there positions had interchanged.Tell the time of shooting.both actual and claimed.

3)..a person bye some cloth from the wholesale at some discount and think when he will sale it at retail price he will get 40% profit.but somehow after selling whole clothes he feels he gets 39% loss.after searching the reason he came to know that the the weight meter is not proper.can u tell how much meter weight and is it more or less from normal.

4)..Jonty went for a movie with hios family but at ticket counter a lot of rush was present.so he was getting upset,then his father told him i m giving u puzzle .

father told him thet here in the line of people,at every third man there was a kid,but the number of man and woman is three times to the number of kids .total people value lie b/w 800 – 1000.tell the number of kids and number of adults.

5)..tom wants to catch a hare .he is standing 250 yards south from the hare.the hare starts moving due east.Tom instead of moving in the northeast direction moves in such a waythat at every instant he is going towards the hare.if speed of tom is 1/3rd that of the hare,find the distance each travelled bfore he caught the hare.

6)..If a farmer buys chicken feed for Â£1.26 per tonne, pig feed for Â£2.74 per tonne and cattle feed for 78p per tonne. How much of each would he have if he had 100 tonnes for Â£100?

7)..A customer at a 7-11 store selected four items to buy, and was told that the cost was $7.11. He was curious that the cost was the same as the store name, so he enquired as to how the figure was derived. The clerk said that he had simply multiplied the prices of the four individual items. The customer protested that the four prices should have been ADDED, not MULTIPLIED. The clerk said that that was OK with him, but, the result was still the same: exactly $7.11. What were the four prices?

9)..What is the largest number which can be obtained as the product of positive integers which add up to 100?

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SET 9

Q1. What is the equation of the line parallel to the line x+3y = -7

and passing through the centroid of the triangle formed by the

intersection of the lines 3x-4y=-11, 3x-y=-5 and 3x+2y=19?.

Q2.A B C have certain mangoes with them. B has 10% less

mangoes than A & C 20% less than A. By what % is the no. of

mangoes with B more than those with C?

Q3.the price of sugar decreased by 20% & then increased by

50%. By what percentage should a housewife now increase or

reduce her consumption so that the expenditure on sugar

remains the same.

Q4.Two children start a two-length swimming race at the same

moment, but from opposite ends of the pool. They swim in lane

and at constant speeds, but one child is faster than the other.

They first pass at a point 18.5 m from the deep end and, having

completed one length, each child is allowed to rest on the edge

of the pool for exactly 45 seconds. After setting off on the return

length, the swimmers pass for the second time just 10.5 m from

the shallow end. How long is the pool?

Q5. A,B and C enter into a partnership invest resp. Rs. 1100, Rs.

1300 and Rs. 1700. After few months an additional capital of Rs.

500 in needed which is invested by B. After 12 months they

closed the business with a profit of Rs. 2527. A’s share of profit

was Rs. 627. B invested the additional capital after,

a.4 months

b.5 months

c. 6 months

d. 8 months

Q6. In a triangle ABC, the internal bisector of the angle A meets

BC at D. If AB=4, AC=3 and angle A= 60 degree, then the length

of AD is:

a. 2 root3

b. (12 root3)/7

c. (15 root3)/8

d. (6 root3)/7

Q7.the price of an item went up by 25% & the family decided to

reduce its consumption so that the total expenditure would

increase by only 8% as compared to the previous expenditure if

25 kg of the item was consumed previously then how many kg of

the item would be consumed now.

Q8. If pqr=1, the value of the expression 1/(1+p+q^-1) + 1/(1+q+r^

-1) + 1/(1+r+p^-1) is equal to

a. p+q+r

b. 1/(p+q+r)

c. 1

d. p^-1 +q^-1 +r^-1

Q9.the price of an item increased by by the same percentage

over the last 4 weeks. If at the beginning it was 512 /gm & in the

end it became 1250/gm find the percentage increase every

week.

Q10. Some boys and two girls are sitting in a row for a

photograph. The probability that girls are sitting together is 1/5.

Find the number of boys?

(a) 10 (b) 4! (c) 8 (d) 2!

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SET 10

Q1 to 10 are in CAT Dose -1

Q11. The rate of inflation of a country is 600% what would be the

cost of an item 4 years from now if its present cost is Rs. 125 &

the rate of inflation remained unchanged throughout.

Q12) A Candle Burns in 6 Hrs. Another Candle of the same

height and width burns in 8 Hrs. After How Many Hours the

height of the first candle will be half of the second Candle?

Q13. When the price of rice falls by 25% a person can buy 10 kg

more for Rs. 300. If the price had fallen by 40%, how much more

rice could he have bought for the same sum?

a. 25 kg

b. 20 kg

c. 12 kg

d. 18 kg

e. 15 kg

Q14. 10 straight lines, no two are parallel and no three of which

passes through any common point, are drawn on a plane. The

total number of regions (including finite and infinite regions) into

which the plane would be divided by the lines is

a. 56

b. 255

c. 1024

d. not unique

Q15. At a bookstore, “TARZAN BOOK HOUSE” is flashed using

neon lights. The words are individually flashed at interval of 2(1/

2), 4(1/4), 5(1/8) seconds respectively, and each word is put off

after a second. The least time after which the full name of the

bookstore can be read again is:

a. 49.5 seconds

b. 73.5 seconds

c. 1744.5 seconds

d. 855 seconds

Q16. After a division of a number successively by 3, 4 and 7, the

reminders obtained are 2, 1 and 4 respectively. What will be the

reminder if 84 divides the same number?

a. 80

b. 76

c. 41

d. 53

Q17. If x, y and z are real numbers such that: x+y+z=5 and xy+yz+

zx=3, what is the largest value that x can have?

a. 5/3

b. root 19

c. 13/3

d. none of these

Q18. Let S denote the infinite sum 2+5x+9x^2 +14x^3+20x^4+….,

where |x|>>Find the remainder whenthe first thousand digits of N(from left)

is divided by 16?

a.7 b.11 c. 13 d. 15

>>Find Remainder when N is divided by 9?

a.8 b.7 c.1 d.0

2)what is sum of the digits of number 4444^4444?

a.5 b.9 c.8 d.7

3)In how many ways can 2310 be expressed as a product of 3 factors?

a. 40 b.41 c.42 d.43

4)In how many ways can 30 (identical in all aspects) balls be

divided into 3 groups?

a.146 b.75 c.130 d.91

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SET 12

Q24. In a 19878 m race Ramu beats bhanu by 9768m. In

98767m race bhanu beats Puru by 4572m. By how many

meters did Ramu beat Puru in a race of 78987m?

a. 7898mm

b. 8909m

c. 40km

d. 8909 km

e. Insufficient data

Q25. Gita flips a fair coin 20 times. Sita flips it 21 times. Sita wins

if she gets more heads that Gita does; else, Gita wins. Note that

Gita wins if there is a tie. What is the probability that Sita wins?

Q26 The Indian cricket team played 25 ODI in a particular

season in a year & won 40% of their matches. A new coach was

brought in who wanted a success rate of 75% of the matches

played by the end of the year. how many minimum matches

more should be played so as to achieve a the target

Q27. If u, v, w and m are natural number such that u^m+v^m=w^

m, then one of the following is true.

a. m>=min(u,v,w)

b. m>=max(u,v,w)

c. m

[…] I did a search of this and found this problem here: assorted cat questions « vasu OA choices are: a) 146 b) 75 c) 130 d) […]

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