Is the positive Integer x a perfect square? 1) Sum of all f

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

Is the positive Integer x a perfect square? 1) Sum of all f

by GMATinsight » Fri Jan 19, 2018 6:32 am

Is the positive Integer x a perfect square?

1) Sum of all factors of x is odd
2) Number of all factors of x is odd

Source: www.GMATinsight.com

Answer: option B

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Source: Beat The GMAT — Data Sufficiency | Fri Jan 19, 2018 6:32 am

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by Scott@TargetTestPrep » Sun Jan 21, 2018 6:31 pm

GMATinsight wrote:Is the positive Integer x a perfect square?

1) Sum of all factors of x is odd
2) Number of all factors of x is odd

We need to determine whether x is a perfect square.

Statement One Alone:

Sum of all factors of x is odd

Statement one alone is not sufficient to answer the question. If x = 4, a perfect square, the sum of the factors is 2 + 4 + 1 = 7; however, if x = 2, not a perfect square, the sum of the factors is 2 + 1 = 3.

Statement Two Alone:

Number of all factors of x is odd

We know that only perfect squares will always have an odd number of factors. For instance 4 has 3 factors: 1, 2, and 4; and 9 has 3 factors: 1, 3, and 9. Thus, since x has an odd number of factors, it's a perfect square.

Answer: B

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