CAT Question Bank (Quant)  Gaurav Sharma  Set 2

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q20) Find the remainder when 1 × 2 + 2 × 3 + 3 × 4 + … + 98 × 99 + 99 ×100 is divided by 101.

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q21) What are the last two digits of (86789)^41?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q22) All the divisors of 360, including 1 and the number itself, are summed up. The sum is 1170. What is the sum of the reciprocals of all the divisors of 360?
a. 3.25
b. 2.75
c. 2.5
d. 1.75

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q23) Last 2 digits of the number (299)^33

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q24) Find the remainder when 1^39 + 2^39 + 3^39 + 4^39 + ... + 12^39 is divided by 39.
a. 0
b. 1
c. 12
d. 38

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q25) Last digit of the LCM of(3^20031) and (3^2003+1) :
a. 8
b. 2
c. 4
d. 6

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q26) What is the remainder when x + x^9 + x^25 + x^49 + x^81 is divided by (x^3  x)?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q27) A number when divided by 8 leaves remainder 3 and quotient Q. The number when divided by 5 leaves remainder 2 and quotient Q + 8. What is the number?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q28)

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q29) In how many ways can 4 distinct balls be distributed into 3 identical boxes?
a) 14
b) 17
c) 11
d) 6

gaurav_sharma last edited by gaurav_sharma
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q30) If Z + 1/Z = 1 then Z^64 + 1/Z^64 = ?
a) 0
b) 1
c) 1
d) 2

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q31) Two friends A and B simultaneously start running around a circular track . They run in the same direction. A travels at 6 m/s and B runs at b m/s. If they cross each other at exactly two points on the circular track and b is a natural number less than 30, how many values can b take?
a) 3
b) 4
c) 5
d) 7

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q32) If  r6 = 11 and 2q12 = 8, then what is the minimum possible value of q/r ?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q33) 'ab' is a two digit number and 'ccb' is a three digit number such that (ab)^2 = ccb, where 'ccb' is greater than 300. What is the value of 'b'?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q34) If a! + (a+1)! has 19 zeroes at the end find value of a

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q35) A number N when divided by a divisor D leaves a remainder of 19. When 3N is divided by D, the remainder is 14. What is the value of D ?
a) 23
b) 37
c) 43
d) 47

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q36) Let N= 2^15 x 3^12. How many factors of N^2 are less than N but do not divide N ?
a) 180
b) 387
c) 207
d) 90
e) 194

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q37) A spherical rubber ball of radius 14 cm is cut by a knife at a distance of “x” cm from its centre, into 2 different pieces. What should be the value of “x” such that the cumulative surface area of the newly formed pieces is 3/28 more than the rubber ball’s original surface area?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q38) How many 3digit numbers have at least 1 even digit?
a) 775
b) 525
c) 800
d) 675

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q39) x, y, z are positive reals such that xyz = 1, x + 1/z = 5, y + 1/x = 29. Find z + 1/y.