# Question Bank - Quant100 - Soumil Jain, CAT Quant 100 percentiler, IIM Calcutta

• Number of Questions - 100
Topic - Quant Mixed Bag
Source - Quant100 Forum

• Q1) Krishna borrows Rs. 45K from a bank at 10% compound interest. He repays it in three annual installments that are in arithmetic progression. He ends up paying 54K totally. How much did he pay in year 1?

• Q2) If two distinct integers a and b are picked from {1,2,3,4....100} and multiplied, what is the probability that the resulting number has EXACTLY 3 factors?

• Q3) 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?

• Q4) How many isosceles triangles with integer sides are possible such that sum of two of the side is 12?
A) 6
B ) 11
C) 17
D) 23

• Q5) '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'?

• Q6) A bartender has two casks full of mixture of vodka and tomato juice. The ratio of vodka and tomato juice in the first and second cask is 3:10 and 8:15 respectively. In what proportion should the mixtures be mixed to satisfy a customer who likes vodka and tomato juice in the ratio 7:16?

• Q7) If | r-6| = 11 and | 2q-12| = 8, then what is the minimum possible value of q/r ?

• Q8) How many numbers have exactly 3 digits when expressed in either base 5 or base 11?

• Q9) How many natural numbers n exist such that ( n! - 2) is the square of a natural number ?

• Q10) If p + q = 13 and pq = 11, find the value of p^3 + q^3

• Q11) 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

• Q12) What is the remainder when (n-1)! - (n-2)! is divided by N ?
a) 0
b) N-1
c) N-2
d) N-3
e) Cannot be determined

• Q13) What is the remainder when (N-2)! + (N-1) is divided by N
a) 0
b) 1
c) 2
d) N-1

• Q14) Find the range of X if |X+3| + 7 > 2|X-4|
a) -2/3 < X < 16
b) -3/4 < X< 18
c) -5/6 < X < 18
d) -2/3 < X< 18

• Q15) 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

• Q16) 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

• Q17) From a pack of well shuffled cards, 20 cards were drawn one after another. N represents the number of different outcomes possible. Find the remainder of N divided by 11.

• Q18) Find the largest power of 100 in the product of all co-primes to 103 that are less than 103

• Q19) In how many ways can 1500 be represented as the product of 3 natural numbers ?

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