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

• Q20) Find the remainder when 1 × 2 + 2 × 3 + 3 × 4 + … + 98 × 99 + 99 ×100 is divided by 101.

• Q21) What are the last two digits of (86789)^41?

• 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

• Q23) Last 2 digits of the number (299)^33

• 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

• Q25) Last digit of the LCM of(3^2003-1) and (3^2003+1) :
a. 8
b. 2
c. 4
d. 6

• Q26) What is the remainder when x + x^9 + x^25 + x^49 + x^81 is divided by (x^3 - x)?

• 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?

• Q28) • Q29) In how many ways can 4 distinct balls be distributed into 3 identical boxes?
a) 14
b) 17
c) 11
d) 6

• Q30) If Z + 1/Z = 1 then Z^64 + 1/Z^64 = ?
a) 0
b) 1
c) -1
d) -2

• 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

• Q32) If | r-6| = 11 and |2q-12| = 8, then what is the minimum possible value of q/r ?

• 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'?

• Q34) If a! + (a+1)! has 19 zeroes at the end find value of a

• 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

• 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

• 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?

• Q38) How many 3-digit numbers have at least 1 even digit?
a) 775
b) 525
c) 800
d) 675

• Q39) x, y, z are positive reals such that xyz = 1, x + 1/z = 5, y + 1/x = 29. Find z + 1/y.

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