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

• Number of Questions - 30
Topic - Quant Mixed Bag
Source - Quant100 Forum

• Q1) 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?

• Q2) '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'?

• Q3) 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?

• Q4) If | r-6| = 11 and | 2q-12| = 8, then what is the minimum possible value of q/r ?

• Q5) How many numbers have exactly 3 digits when expressed in either base 5 or base 11?

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

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

• Q11) 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

• 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 co-primes 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 two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a two-wheeler 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)?

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