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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Is square root of a positive integer x an integer? tagged by: M7MBA ##### This topic has 1 expert reply and 0 member replies ## Is square root of a positive integer x an integer? 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. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 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. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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