# CAT Question Bank (Quant) - Gaurav Sharma - Set 2

• Q60) There are two fixed poles on the opposite sides of a road at points A and B. The height of one of the poles is 70% of AB and the height of the other pole is 40% of AB. A point on AB is equidistant from the top of the two poles. What is the distance of this point from the foot of the shorter pole?
(a) 66.5% of AB
(b) 65.5% of AB
(c) 68.0% of AB
(d) 67.5% of AB

• Q61) Remainder when 1^7 + 2^7 + 3^7 + ... + 100^7 is divided by 7

• Q62) In a community of 100 students, each student studies one or more of the two subjects viz. Mathematics and Chemistry. The number of students studying Mathematics is greater than the number of students studying Chemistry which is greater than the number of students studying both Mathematics and Chemistry. What is the maximum number of students who study Chemistry?
(a) 97
(b) 49
(c) 98
(d) 50

• Q63) Sixty equally spaced line segments are drawn on a circular clock such that each line segment is a radius of the circle. If the minute hand and the hour hand of the clock overlap with one of these line segments at 12 Noon, then at what time during the next 12 hours will the minute hand overlap with the line segment which is immediately prior to the line segment with which the hour hand overlaps?
(a) 4 : 24 P.M.
(b) 2 : 12 P.M.
(c) 9 : 48 P.M.
(d) Cannot be determined

• Q64) Let a, b and c be the sides of a triangle ABC. If (a + b + c) (b + c – a) = kbc, then k lies between
a) -1 to 1
b) 0 to 4
c) -4 to 4
d) 4 to 6

• Q65) A three-digit positive number ‘X’ is in the decimal system. ‘X’ is equal to cube of its unit digit as well as square of a two digit number formed by the remaining two digits(in any order). Find the sum of the digits of ‘X’.

• Q66) Jose is an avid reader. He wants to order some books on mathematics, History and Literature from an e-commerce website. In how many ways can he order at least one book each on Mathematics, History and Literature from 3 distinct books on Mathematics, 4 distinct books on History and 5 distinct books on Literature?
a) 4096
b) 3255
c) 4095
d) 2520

• Q67) The average age of a group of 30 people is 40 years. Kay, whose present age is 11 years, had joined the group two years ago. What was the average age (in years) of the remaining 29 people (excluding Kay) two years ago?
(a) 37
(b) 38
(c) 40
(d) 39

• Q68) How many two digit numbers are there such that sum of reciprocals of all of its factors is 2 ?

• Q69) If 20 units of item A are sold at a profit of x% and 30 units of item B are sold at a profit of 2x%, then what is the net profit percentage?
a) 1.4x %
b) 1.6x %
c) 1.5x%
d) Data Insufficient

• Q70) A watch, which gains time uniformly, was 5 minutes behind the correct time when it showed 11:55 AM on Monday. It was 10 minutes ahead of the correct time when it showed 06:10 PM on the next day. When did the watch show the correct time?
(a) 6 AM, Tuesday
(b) 6 PM, Monday
(c) 2 PM, Tuesday
(d) 10 PM, Monday

• Q71) Two jars contain milk and water in the ratio 7 : 3 and 3 : 2 respectively. In what ratio should the contents of the two jars be mixed such that the final ratio of milk and water in the resultant solution becomes 23 : 17?
(a) 1 : 3
(b) 1 : 5
(c) 3 : 5
(d) Data Inconsistent

• Q72) Two litres of a solution having water and milk in the ratio 3 : 5 is mixed with three litres of another solution having water and milk in the ratio 5 : 3. What is the ratio of water and milk in the resultant mixture?
(a) 18 : 23
(b) 1 : 1
(c) 19 : 21
(d) 21 : 19

• Q73) If A= (1 + 1/38)^38 and B = (1 + 1/37)^37 then
a) A = B
b) A > B
c) A > 4
d) A < B

• Q74) If two natural numbers, each of which is a 2-digit, are chosen randomly, find the probability that these two numbers have the same unit digits.

• Q75) If x + 1/x = root 3, find x^55 + 1/x^55 = ?

• Q76) Ram Prasad lives in Ramnagar colony where each house has a number. If Ram Prasad’s house number is a multiple of 7, then it falls between 200 and 299. If his house number is not a multiple of 4, then it falls between 300 and 399. If his house number is not a multiple of 9, it falls between 400 and 499. His house number can be
a) 432
b) 252
c) Neither a nor b
d) Both a and b

• Q77) A bus covers a journey at an average speed of 90 km/h. If the time for which the bus stops during the journey is excluded, then the average speed for the journey becomes 108 km/h. For how much time, on an average, does the bus stop every hour?
(a) 12 minutes
(b) 10 minutes
(c) 15 minutes
(d) 7.5 minutes

• Q78) x and y are real numbers such that y = |x – 2| – |2x – 12| + |x – 8 |. What is the least possible value of y?
(a) 6 3
(b) 2
(c) –2
(d) None of these

• Q79)
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