# CAT Question Bank - Co Primes

• Q5) For N = 2^5 * 3^2* 5^4 * 7 * 11^3, find the number of ways to write N as a product of three numbers such that these numbers are overall coprime (not only pairwise)

• Q6) How many three digit numbers less than 200 are coprime to 638?

• Q7) Number of natural numbers smaller than N & coprime to N is 84. Find

1. All possible values of N.
2. Least possible value of N.
3. Greatest possible value of N

• Q8) There are ten distinct rational numbers and the sum of any nine of them is an irreducible proper fraction having denominator 22. If the sum of these ten rational numbers is p/q, where p and q are coprime numbers, then find the value of p + q.

• Q9) If a and b are coprime to each other, then what will be the largest possible greatest common divisor of a + 201b and 201a + b.

• Q10) How many ordered pair (a,b) are possible if a + b = 1300 and a, b are coprime ?

• Q11) HCF of three numbers is 6 and their sum is 120. How many such triplets exist?

• Q12) How many positive integers less than 100 share a common factor with 100 other than 1

• Q13) If a & b are coprime, how many pairs of (a, b) are possible if a + b = 9

• Q14) Find the total number of pairs (a, b) such that HCF (a, b) + LCM (a, b) = 91

• Q15) Find the value of the 80th smallest positive integer that is coprime to 9955.

• Q16) In how many ways can we express 83 as the sum of two coprime numbers

• Q17) In how many was can we write 540 as the product of 3 coprime numbers

• Q18) How many numbers below 100 are coprime to 100 but not co prime to 1500?

• Q19) Number of non negative integer solutions for a + b + c = 20, where a, b and c are coprimes.

• Q20) How many integer pairs (a, b) are possible if LCM (a, b) = 540

• Q21) Let S = { 1, 2, 3, 4, ... 1000}. Let A be subset of S such that any two elements in A are coprime to each other and no element of A is a prime. The maximum possible number of elements in A is
a. 31
b. 30
c. 12
d. 11
e. None of These

• Q22) a, b and c are natural numbers such that a + b + c = 219, what is the maximum possible difference between LCM of any two possible triplets (a, b, c) ?

• Q23) Sum of two numbers is 85 and their LCM is 102. Find the numbers

• Q24) Atleast how many numbers should be taken from the set {1, 2, 3, ..., 50} to ensure that two of the selected numbers are coprime

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