Integers

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Ramit88: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Fri Nov 26, 2010 8:25 am; Thanked: 3 times

by Ramit88 » Thu Jan 20, 2011 2:28 am

If n and y are positive integers and n represents the no. of different positive factors of y , is y a perfect square?

1. sqrt(n) is an odd int
2. y = sqrt{5^[2(n-1)]}

ANS A

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Source: Beat The GMAT — Data Sufficiency | Thu Jan 20, 2011 2:28 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Jan 20, 2011 3:31 am

Ramit88 wrote:If n and y are positive integers and n represents the no. of different positive factors of y , is y a perfect square?

1. âˆšn is an odd int
2. y = âˆš[5^{2(n-1)}]

If an integer is not perfect square, then the number of different positive factors of that integer is always even. And if it is a perfect integer, then the number of different positive factors of that integer is always odd.

Statement 1: âˆšn is an odd integer.
Hence n is also an odd integer. Thus y must be a perfect square.

Sufficient

Statement 2: y = âˆš[5^{2(n-1)}] = 5^(n - 1)
For y to be a perfect square, âˆšy must be an integer.
Thus, âˆš(5^(n - 1)) must be an integer. Which is only possible when (n - 1) is even. But we don't know anything about n.

Not sufficient

The correct answer is A.

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