CAT Question Bank (Quant)  Gaurav Sharma  Set 1

Q49) Mr. Mehra is planning for higher education expenses of his two sons aged 15 and 12. He plans to divide Rs 15 lakhs in two equal parts and invest in two different plans such that his sons may have access to Rs 21 lakhs each when they reach the age of 21. He is looking for plans that will give him a simple interest per annum. The rates of interest of the plans for his younger son and his elder son should be
A. 5% and 7.5% respectively
B. 8% and 12% respectively
C. 10% and 15% respectively
D. 15% and 22.5% respectively
E. 20% and 30% respectively

Q50) The lengths of the three edges of a cuboid are increased by a%, b% and c%. The volume increases by V%, where V is an integer. How many values can V take if a, b, c are real numbers and 10 ≤ a, b, c ≤ 20?
(a) 11
(b) 39
(c) 41
(d) Cannot be determined

Q51) After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percent above the cost price does he mark his goods?

Q52) A three digit nonzero number 'abc' in base 5, when converted to base 7, becomes 'cba'. Which of the following is necessarily true?
a) a must be 2
b) c must be 2
c) b must be 0
d) None

Q53) If number of students a class is firstly increased by a% then decreased by b% then there is no change in number of students then ba = ?
a. a * b
b. b – a
c. a * b/100
d. (a+b)/100
e. NoT

Q54) 4n has twice the number of factors as n. Which of the following could be the remainder when n is divided by 8?
(1) 2
(2) 3
(3) 4
(4) 5

Q55) A is the set of positive integers such that when divided by 2, 3, 4, 5, 6 leaves the remainders 1, 2, 3, 4, 5 respectively. How many integers between 0 and 100 belong to set A?
a. 0
b. 1
c. 2
d. None of these

Q56) What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?
a) 1 or 7
b) 2 or 14
c) 3 or 21
d) 4 or 28

Q57) A natural number when increased by 50% has its number of factors unchanged. However when the value of number is reduced by 75% the number of factors is reduced by 66.66%..One such number could be
a) 32
b) 84
c) 126
d) NOT

Q58) Natural number 'a' is the smallest of 50 consecutive natural numbers. If the sum of these 50 numbers is a perfect square, how many different values of 'a' are possible?
a) Zero
b) One
c) Two
d) More than two

Q59) In a class of 60 students, the average age of the 25 girls is 12 years and that of the boys is 18 years.Three of the students aged 18, 19 and 20 years leave the class and are replaced by 4 students of ages 10, 11, 10 and 11 years. Find the change in the average age of the class .
a) 0.167 years
b) 0.25 years
c) 1.2 years
d) 0.5 years

Q60) In how many ways can 18 identical white balls and 16 identical black balls be arranged in a row so that no two black balls be together ?

Q61) What would be last two digits of (451^41)  (41^451) ?

Q62) 5 points selected on circumference of circle. Find probability that they lie in same semicircle.

Q63) From a point in the interior of an equilateral triangle, the perpendicular distances of the sides are, √3 cm, 2√3 cm and 5√3 cm. The perimeter (in cm) of the triangle is
a. 48
b. 51
c. 57
d. 63

Q64) The product of digit is a Factor of a two digit number. Number of such digit are:
a. 3
b. 5
c. 9
d. 27

Q65) Through each vertex of a triangle, a line parallel to the opposite side is drawn. The ratio of the perimeter of the new triangle thus formed with the original triangle is,
a. 3:1
b. 2:1
c. 3:2
d. None

Q66) What will be the effect on its area of a triangle if it’s height is decreased by 40% and it’s base is increased by 40%?
a) No change
b) 8% decrease
c) 16% decrease
d) 16%increase

Q67) A regular hexagon is formed by cutting the corners of sides of an equilateral triangle of side 6 cm.The area of this hexagon will be

Q68) The lengths of three medians of a triangle are 9 cm, 12 cm and 15 cm. The area (in sq cm) of the triangle is
a. 72
b. 83
c. 94
d. None