XAT 2025 Number System Question (Medium)

Question

Arun selected an integer x between 2 and 40, both inclusive. He noticed that the greatest common divisor of the selected integer x and any other integer between 2 and 40, both inclusive, is 1. How many different choices for such an x are possible?

Optima Learn · Accepted Answer

We want integers x between 2 and 40 such that gcd x, y 1 for every other integer y in 2, 40 , y x. If x is composite, it has a prime factor p. Then some other integer y in 2, 40 will be a multiple of p and not equal to x , so gcd x, y p 1. Hence x cannot be composite. So x must be prime. Let x p be

XAT 2025 Number System — Previous Year Question

XAT 2025

Quantitative

Number System

Medium

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