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

Number of Questions  100
Topic  Quant Mixed Bag
Answer Key available?  No
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  r6 = 11 and  2q12 = 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 (n1)!  (n2)! is divided by N ?
a) 0
b) N1
c) N2
d) N3
e) Cannot be determined

Q13) What is the remainder when (N2)! + (N1) is divided by N
a) 0
b) 1
c) 2
d) N1

Q14) Find the range of X if X+3 + 7 > 2X4
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 coprimes to 103 that are less than 103

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