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# If k is a positive integer, is k the square of an integer?

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Intern
Joined: 05 Nov 2008
Posts: 6
If k is a positive integer, is k the square of an integer? [#permalink]

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05 Nov 2008, 20:19
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If k is a positive integer, is k the square of an integer?
(1) k is divisible by 4.
(2) k is divisible by exactly 4 different prime numbers.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
SVP
Joined: 17 Jun 2008
Posts: 1529

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05 Nov 2008, 21:36
E.

From stmt1: K has 2^2 as the factor. However, K may also have 3, 4, 3^3, 4^2, etc. as factors. Insufficient.

From stmt2: K has four different prime factors. However, it does not say that it has only four different prime factors. For example, K = 2*3*5*7 or, K = 2^2*3^2*5^2*7^2. Insufficient.

Combining both statements too,
K = 2^2*3*5*7 or K = 2^2*3^2*5^2*7^2.
Re: integer--30   [#permalink] 05 Nov 2008, 21:36
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# If k is a positive integer, is k the square of an integer?

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