CAT Question Bank (Quant)  Gaurav Sharma  Set 2

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q40) A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?
a. 34%
b. 44%
c. 54%
d. 64%

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q41) A circle is inscribed in an isosceles trapezoid with bases 8 and 18. What is the area of the circle?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q42) Trapezoid ABCD is inscribed in a circle. Parallel sides AB and CD are 7 inches apart and 6 and 8 inches long, respectively. What is the radius of the circle in inches?
a) 4
b) 5
c) 4 root2
d) 5 root2
e) 7

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q43) A train starts from Delhi at a : b o’clock (i.e. ‘b’ minutes after a o’clock). It reaches Chandigarh on the same day at b : c o’clock after taking exactly ‘c’ hours and ‘a’ minutes. How many different values of a are possible? All the times are given in 24hour clock format.
(a) 0
(b) 1
(c) 2
(d) 3

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q44) What is the smallest value of x for which x! is divisible by 3^7?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q45) A triangle is called a ptriangle if the length of each of its side (in units) and its area (in sq. units) are integers. How many of the triangles with the sides (in units) given below are ptriangles?
(i) 4, 5 and 6
(ii) 3, 4 and 5
(iii) 5, 8 and 9
(iv) 5, 6 and 8
(a) One (b) Two (c) Three (d) Four

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q46) Two friends – Prakash and Arpit – started running simultaneously from a point P in the same direction along a straight running track. The ratio of the speeds of Prakash and Arpit was 2 : 5 respectively. Two hours later, Arpit turned back and started running backwards at onefifth of his original speed. He met Prakash at a distance of 10 km from the point P. What was Prakash’s running speed?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q47) A tank has four inlet pipes such that each inlet pipe while working independently can fill the tank in 4 hours. The tank also has two outlet pipes such that each outlet pipe while working independently can empty the tank in 3 hours. If all the six pipes are opened simultaneously, then in how much time will the tank get filled completely?
(a) 2.0 hours
(b) 3.0 hours
(c) 2.5 hours
(d) 7.0 hours

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q48) A cubical container is half filled with water. The container is now inclined in such a way that the water surface touches one edge completely and does not touch the other lateral face of the cube which it was touching before inclination.What is the angle made by the surface of water with the bottom surface of the container?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q49) The average market price of three shares A, B and C is Rs. x. Shares A and C lose Rs. y each and B gains Rs.y/2. As a result, the average market price of the three shares decreases by Re. 1. The value of y is
(a) 2
(b) 3
(c) 4
(d) dependent on x

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q50) Let f(x) = ax^2 + bx + c, where a, b and c are real numbers and a ≠ 0. If f(x) attains its maximum value at x = 2, then what is the sum of the roots of f(x) = 0?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q51) x/y = 19.636363...... and x and y are coprime, then find x + y

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q52) If LCM of numbers from 1 to 20 is N then find the LCM of numbers from 1 to 35

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q53) 'ab' is a twodigit prime number such that one of its digits is 3. If the absolute difference between the digits of the number is not a factor of 2, then how many values can 'ab' assume?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q54) A and B start running simultaneously on a circular track from point O in the same direction. If the ratio of their speeds is 6 : 1 respectively, then how many times is A ahead of B by a quarter of the length of the track before they meet at O for the first time?
(a) 4
(b) 5
(c) 7
(d) 10

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q55) There are 3 solutions
Solution 1: Consists of A and B in the volume ratio 3 : 2.
Solution 2: Consists of B and C in the volume ratio 1 : 4.
Solution 3: Consists of B and C in the volume ratio 7 : 3.
The 3 solutions are mixed in the volume ratio X : 3 : 2. If the percentage composition of A and B are equal in the resultant mixture, then what is the value of X?
(a) 4
(b) 5
(c) 10
(d) 11

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q56) How many fivedigit numbers can be formed so that at even place there is an even digit and at odd place there is an odd digit, repetition of digits is not allowed? (Assume zero is an even number)

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q57) 2^29 is a nine digit number with each distinct digit. Which digit is not used?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q58) What is the smallest positive integer ‘k’ such that C(2k, k) is divisible by 200?
(a) 23
(b) 61
(c) 13
(d) 11

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q59) In the Adams family, the average weight of the 70 family members is 60 kg. The ratio of the total number of men to the total number of women is 9 : 5, and the ratio of the average weight of women to the average weight of men is 5 : 7. Find the average weight of the women (in kg).