The quantitative part on TCS

QUANTITATIVE APPTITUDE

36. A number consists of two digits whose sum is 7. If the digits are reversed then the number is increased by 27. The number is-
a) 25 b) 34 c) 16 d) 52

sol :- (a) Let the number be 10x + y.
therefore x + y = 7 &
10y + x = 10x + y +27
è y = 5 , x = 2
therefore the number 10x + y =25.

37 The least number which when divided by 12, 15 , 20 & 54 leaves in each case a remainder of 8 is-
a) 536 b) 544 c) 548 d) 504

sol :- (c) L.C.M of 12 ,15 , 24 & 54 = 540
therefore Reqd. number = 540 + 8 =548.

38 he population of certain village increased by 5 percent anually. Its present population is 8000. The population after three years will be -
a) 8261 b) 9261 c) 9161 d) 9200

sol :- (b) population after three years
= 8000( 1 + (5/100) )3
8000 * 21/20 * 21/20 * 21/20 = 9261

39 A passanger train running at a speed of 80 Km/hr leaves the railwaystation 6 hours after a goods train leaves and overtakes in 4 hours . The speed of goods train is-
a) 32 Km/hr b) 40 Km/hr c) 50 Km/hr d) 60 Km/hr

sol :- Let speed of goods train be x Km/hr
therefore 10x = 320
è x = 32.

40 The average age of the mother and her 6 children is 12 years , which is reduced by 5 years if the age of the mother is excluded . How old is the mother.
a) 42 b) 40 c) 48 d) 50

sol:- (a) Total age of mother and 6 children = 12 * 7 = 84
Total age of 6 children = 7 * 6 = 42 years.
Mothers age 84 - 42 = 42 years.

41 Which one number can be placed at the sign of interrogation ? (read row wise).

4 6 3 8
2 8 4 4
6 5 ? 10
a) 3 b) 6 c) 8 d) 10

sol :- (a) In each row è first numbr * second number = third number * fourth number.

42 If the day before yesterday was Saturday . what day will fall on the day after tomorrow.
a) Friday b) Thursday c) Wednesday d) Tuesday

sol :- (c) If day before yesterday was Saturday , so today is Monday.
Thus day after tomorrow will be Wednasday.

43 man completes 5/8 of a job in 10 days . At this rate how many more days will it take to complete the whole job.
a) 5 b) 6 c) 7 d)71/2

sol :- (b) 5/8 of the job is done in 10 days
therefore remaining 3/8 of the job is done in 10* (8/5) * (3/8) = 6 days.

44 Suppose six coins are flipped then the probability of getting atleast one tail is
a) 71/72 b) 53/54 c) 63/64 d) 1/12

sol :- (c) Total number of events 26 = 64
probability that no tail occurs = 1/64
probability of occuring atleast one tail = 1 - (1/64) = 63/64.

45 A's age is 1/6 of B' age will be twice of A's age after 10 years. If C's eight birthday was celebrated two year ago, then the present age of A must be.
a. 5 year
b. 10 years
c. 15 years
d. 20 years

Ans : (a) A=(1/6)B
B+10=2(C+10)
C=10
Therefore, B=30, A=5

46 the denominator of a rational number is 3 more than its numerator. If the numerator is increased by 7 and the denominator is decreased by 2 , we obtain 2. The rational number is.
a. 1/4
b. 5/8
c. 7/10
d. 8/11

Ans: (b) let the rational number is p/q
Therefore, q=p+3
Therefore, (p+7)/(p+3-2)=2
P+7=2p+2
P=5
Having rational number is = 5/8

47 5% income of A is equal to 15% income of B is equal to 20% income of C. If the income of C is Rs 2000, then the total income of A,B and C (in rupees) is.
a. 6000
b. 9000
c. 12000
d. 18000

Ans : (d) 5% of A= 15% of B
=>5A = 15B = 20% of C
=>10% of B = 20% of C
=>10B = 20
=>B=2C
if C=2000, then B=4000
therefore, A=12000
Hence, the total income of A,B and C=18000

48 The arerage of marks obtained by 120 candidates was 35. If the average of the passed candidates was 39 and that of the failed candidates was 15, then the number of those candidates, who passed the examination, was
a. Rs 100
b. Rs 110
c. Rs 120
d. Rs 150

Ans : (a) Therefore the number of candidates passed =x
Therefore, 39x+15(120-x)=120*15
ð 24x = 120 * 35 - 120*35
ð = 120(35-15)
ð = 120*20
ð x = 100

49 certain job was assigned to a group of men to do in 20 days. But 12 men did not turn up for the job and the remaning men did the job in 32 days. The orginal number of men in the group was.
a. 32
b. 34
c. 36
d. 40

Please this easy one if you still cannt do it ask me do it

50) In an election between 3 contestants, the winner gets 20 votes more than his nearest rival and 35 votes more than the third candidate. The winner and the first runner up polled an average 90 votes each. Find the total number of votes cast [Assume there are no invalid votes

1) 245 2) 260 3)275 4) 290

Answers
Let the number of votes polled be =x, x-20, x-35
X+(x-20)/2 =90

Thus x=100
Total vote =100+80+ 65=245

51) In a chess tournament, each of the 6 players will play every other player exactly once. How many matches will be played during the tournament ?

a)12 b)15 c)30 d)36

ans) b : 5+4+3+2+1=15

52) A wheel makes 1000 revolutions in covering a distance of 88 Km. The dimete of the wheel is.
a. 24 m
b. 40 m
c. 28 m
d. 14 m

Ans : (c) let the dimeter of the wheel be 2r
Therefore, 2(pie)r*1000=88000
ð 2*(22/7)*r*1000=88000
ð r=14
Dimeter of the wheel = 28m.

53) A tradesman b is means of false balance defrauds to the extent of 8% in buying goods and also defraunds to the extent of 8% in selling. His gain percent is.
a. 16%
b. 15.48%
c. 16.64%
d. 36%

Ans : (c) The tradesman pays for 100 kg nd 108 kg of goods by means of false balance.
Actually, he sells 108 Kg of goods, but due to false balance, he sells 116.64 Kg of goods.

54) A two digit number is such that the product of the digits is 8. When 18 is added to the number , then the digits are reversed. The number is
a. 18
b. 24
c. 82
d. 42

Ans: (b) let the number be 10x + y
Therefore , xy = 8 .............(i)
10x + y + 18 = 10y + x
ie, 9x - 9y = - 18
ie, x - y = - 2.................(ii)
therefore, (x +y)2=4xy + (x - y)2
ð 32 + 4 = 36.................(iii)
(ii) and (iii) , given x = 2, y = 4
hence the number is 24

55) 1/1+a(n-m) + 1/1+ a(m-n) is equal to
a. 0
b. 1
c. 1/3
d. a(m+n)
( the subcripts will be displayed, plz adjust)

Ans : (b) 1+an/am
1+ am/an
=>am/am+an + an/am+an=1

56 -57 :-Let Jayant's age be x and Mira's age be (x + y). When Mira was x, Jayant was (x - y). When Mira was 3(x - y), Jayant was (3x - 4y). When Mira was 2(3x - 4y), Jayant was (6x - 9y). When Jayant was (x + y)/2 , Mira was (x + 3y)/2; half of which is (x + 3y)/4. Hence, (x + 3y)/4 = 6x - 9y.Hence, 23x = 39y. Hence x = 23, y = 39 and x + y = 62.

Sol 58 - 59:- Suppose the man had x children, and each received y one dollar bills, then (402 - x)/x = xy. Hence 402/x = xy + 1. Hence, x must be a factor of 402 = 2 * 3 * 67. Since the man has 3 sons, x>= 3. The only possible values are 3 and 6, then 402/x = 134, xy = 133, and y is not an integer. If x = 6, then 402/x = 67, xy = 66 and y = 11. Hence x = 6.

60) c

61) For what value of 'a' is the expression 2x3 -3x2+7x+_a is divisible by x+1
a) 7 b) 12 c) 6 d)18

ans: (b)
f(x) = 2x3 - 3x2 + 7x + a
f(-1) = 2(-1)3 - 3(-1)2 + 7(-1) + a
a = 12

62) The side of a square increases by 10%. Find the increase in the area.
a)100% b) 10% c) 20% d) 21%

ans: (d)
let side be 10, therefore, area = 100
side after increase = 11, therefore, area = 121, increase is 21%

63 )Which is the largest of the following fractions
a)13/17 b) 9/13 c) 5/9 d)17/21

ans: (d)
when the difference between numerator and denominator is same across fractions, the fraction with the biggest denominator is the largest

64 )Three dies are tossed. What is the probability that a total of 3 comes up?
a)1/36 b)1/18 c) 3/216 d)1/216

ans: (d)
there are 216 different ways in which the dice may fall. However only 1 combination can result in a sum of 3 i.e. (1,1,1)

65)simplify x3+y3+x2y+y2x
x2+y2
a) x+y b) x-y c) x2y d) xy2

ans: (a)
Eq = x2(y+x) + y2(y+x)/x2 + y2

= (x2+y2)(x+y)/x2+y2 = x + y

66) The reverse of a two-digit number is 45 less than the number itself. What is the number?
a) 45 b) 27 c) 72 d) 16

ans: (c)
There are various sets of numbers whose reverse of digits results in a difference of 45. From the alternatives, 27, 72 and 16 fit the condition. However, as the number is bigger than the reverse, the answer is 72.

67) A rope is 1/3 brown, 2/5 black and the remaining 3 meters is yellow. What is the length of the rope?
a) 15 mts b) 10.5 mts c)11.25 mts d) 12.8 mts

ans: (c)
if length is 'x', the yellow is
x - x/3 - 2x/5 = 3
15x - 5x - 6x/15 = 3
x = 45/4 = 11.25meters

68) A merchant losses 10% on selling a horse. Had sold it for Rs100 more he would have gained 10% more. Whatis his cost price?
a) 500 b) 550 c) 450 d) 525

ans: (a)
20% = Rs.100
Therefore, 100% = Rs.500

69) Simplify a2-b2 _ a3-b3
a-b a2-b2
a) ab b) ab c) 1 d) ab
a+b a-b a-b

ans: (a)
(a2 - b2)/(a-b) - (a3 - b3)/(a2-b2)
= (a+b) - (a2+ab+b2/a+b)
= (a+b)2 - (a2+ab+b2) / (a+b)
= (a2+b2+2ab-a2-ab-b2)/(a+b)
= ab/a+b

70) In an examination there are two groups each containing 4 questions .a candidate
is required to attempt 5 questions from any group .In how many ways can 5
questions be attempted .
a) 24 b) 48 c) 96 d) none of these

sol :- 4C3 * 4C + 4C2 * 4C3 = 4 * 6 + 4 * 6 = 48.

.71) A number which when multiplied by 11 becomes as much above 180 as it was below
180 . find the number
a) 20 b) 30 c) 25 d) 35

sol :- (b) let the number be x
11 x = 180 + y
and x = 180 - y
è x = 30 , y = 150
therefore required number is 30

72 (c ), use the method of allegation , if you donot know the method do learn this, if you donot know, do yourself a favour ask me.

73. 2835=5*7*34

1092=22 * 3 * 13 * 7 , GCD = 7 * 3 = 21

Ans: (c)

74. (x - 1/x)2 = 16

x2 + 1/x2 - 2 = 16
therefore, x2 + 1/x2 = 18

Ans: (a)

75. AB = 3x, BC = 4x
AC = (3x2 + 4x2)1/2 = 5x cm, perimeter = 12x
Given perimeter = 24,
Therefore, x = 2 and AC = 10

Ans: (c)