CAT Question Bank - Co Primes

[Rowdy Rathore]

Number of Questions - 30
Topic - Co-Primes
Answer key available? - No
Source - Curated Content

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Q1) How many integers from 101 to 300 are coprime to 20 ?

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Q2) How many positive integers between 100 and 200 are coprime to 630 ?

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Q3) Number of ways in which 480 can be written as the product of two numbers which are coprime to each other

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Q4) How many factor pairs of N = 360 will be coprime to each other?

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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)

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

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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

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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.

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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.

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

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

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

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

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

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

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

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

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

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