Quant Boosters  Soumil Jain, CAT Quant 100 percentiler, IIM Calcutta  Set 1

Q6) How many natural numbers n exist such that ( n!  2) is the square of a natural number ?

Q7) If p + q = 13 and pq = 11, find the value of p^3 + q^3

Q8) 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

Q9) What is the remainder when (n1)!  (n2)! is divided by N ?
a) 0
b) N1
c) N2
d) N3
e) Cannot be determined

Q10) What is the remainder when (N2)! + (N1) is divided by N
a) 0
b) 1
c) 2
d) N1

Q11) 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

Q12) 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

Q13) 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

Q14) 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.

Q15) Find the largest power of 100 in the product of all coprimes to 103 that are less than 103

Q16) In how many ways can 1500 be represented as the product of 3 natural numbers ?

Q17) N = X^Y, where X=12345.......737475 and Y=12345.......484950. Find the remainder when N is divided by 32.
a) 9
b) 19
c) 25
d) 17

Q18) How many five digit numbers with distinct digits exist such that first 3 digits are in ascending order and last 3 are in descending order ?

Q19) Of the 200 candidates who were interviewed for a position at a call center, 100 had a twowheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a twowheeler and a credit card, 30 had both, a credit card and a mobile phone and 60 had both, a two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?

Q20) For all non  negative integers x and y, f(x, y) is defined as below.
f(0, y) = y + 1;
f(x + 1, 0) = f(x, 1);
f(x + 1, y + 1) = f(x, f(x + 1, y)).
Then what is the value of f(1, 2)?

Q21) N is a 3digit number that is a multiple of 7; what is the probability that it will be a multiple of 5?

Q22) All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will contain zero's?

Q23) In how many ways can two numbers be selected from the set A= { 1,2,3.....50} such that the sum of the numbers is a multiple of 3 ?

Q24) How many natural numbers upto 9999 are divisible by 5 or 13 or 17 ?

Q25) In how many ways can 12 books be equally divided into 3 identical parcels ?