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Is square root of a positive integer x an integer?

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Is square root of a positive integer x an integer?

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Is square root of a positive integer x an integer?

(1) The sum of distinct factors of x is odd
(2) x has an odd number of distinct factor

The OA is B .

Experts, is there a formula I should use here? I don't know how to solve this DS question.

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M7MBA wrote:
Is square root of a positive integer x an integer?

(1) The sum of distinct factors of x is odd
(2) x has an odd number of distinct factor

The OA is B .

Experts, is there a formula I should use here? I don't know how to solve this DS question.
Statement 1: x could be 2, as 1 + 2 = 3, which is odd; The square root of 2 is not an integer, so we have a NO.
x. could be 4, as 1 + 2 + 4 = 7, which is odd. The square root of 4 is an integer, so we have a YES.
S1 alone is not sufficient.

Statement 2: A perfect square, by definition, has an ODD number of factors. (This makes sense. If we're thinking about pairs of integers that multiply to a perfect square, such as, say 4, we'd have 1*4 or 2*2. Because one of the pairs involves multiplying a number by itself and everything else involves two distinct factors, a perfect square must have an ODD number of factors.) Thus, if we know that a number has an ODD number of factors, we know we're talking about a perfect square, and so the answer to the question is YES, no matter what we pick, the square root of this value will always yield an integer. Statement 2 alone is sufficient to answer the question. The answer is B.

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