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# If x is a positive integer, is x prime?1) x has the same number of factors as y2, where y is a positive integer greater than 2.2) x has the same number of factors as z, where z is a positive integer greater than 2.a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer? Related Test: Test: Prime Numbers- 1

## GMAT Question

If x is a positive integer, is x prime?

(1) x has the same number of factors as y^2, where y is a positive integer greater than 2.

y^2 is a perfect square. The number of distinct factors of a positive perfect square is ALWAYS ODD, while the number of factors of a prime is two (1 and itself). Thus since x has the same number of factors as a perfect square it cannot be a prime. Sufficient.

(2) x has the same number of factors as z, where z is a positive integer greater than 2. Clearly insufficient.

 Talent Skill Learning Aug 07, 2021
(1) x has the same number of factors as y2, where y is a positive integer greater than 2.

y2 is a perfect square. The number of distinct factors of a positive perfect square is ALWAYS ODD, while the number of factors of a prime is two (1 and itself). Thus since x has the same number of factors as a perfect square it cannot be a prime. Sufficient.

(2) x has the same number of factors as z, where z is a positive integer greater than 2. Clearly insufficient.