CAT Question Bank (Quant) - Gaurav Sharma - Set 1
Q46) In a square PQRS, A and B are two points on PS and SR such that PA = 2AS, and RB = 2BS If PQ = 6, the area of the triangle ABQ is (is it a repeat)
gaurav_sharma last edited by gaurav_sharma
Q47) Ram, Shyam and Hari went out for a 100 km journey. Ram and Hari started the journey in Ram’s car at the rate of 25 kmph, while Shyam walked at 5 kmph. After sometime, Hari got off and started walking at the rate of 5 kmph and Ram went back to pick up Shyam. All three reached the destination simultaneously. The number of hours required for the trip was:
Q48) How many whole numbers between 100 and 800 contain the digit 2?
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?
(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 non-zero 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
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 |b-a| = ?
a. a * b
b. b – a
c. a * b/100
Q54) 4n has twice the number of factors as n. Which of the following could be the remainder when n is divided by 8?
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?
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
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?
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
Q64) The product of digit is a Factor of a two digit number. Number of such digit are:
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,