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If x is an integer, what is the value of x? (3) [#permalink]

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17 Nov 2008, 14:41

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If √x is an integer, what is the value of √x? (3) 11<x<17 (4) 2<√x<5 ________________________________________________________________ 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.

(1) is insufficient due to the fact that 16 has two roots, +- 4. I would be surprised if GMAT would only consider the positive root, as I think it is incomplete to say that sqrt(16)=4 rather than +-4. When you take a square root, you are asking: which number, when squared, gives the desired result? For 16 there are clearly two answers and neither one alone is complete.

(2) is also insufficient by itself since sqrt(x) could be 3 or 4.

Together, (1) and (2) show that the answer is sqrt(x)=4.

(1) is insufficient due to the fact that 16 has two roots, +- 4. I would be surprised if GMAT would only consider the positive root, as I think it is incomplete to say that sqrt(16)=4 rather than +-4. When you take a square root, you are asking: which number, when squared, gives the desired result? For 16 there are clearly two answers and neither one alone is complete.

(2) is also insufficient by itself since sqrt(x) could be 3 or 4.

Together, (1) and (2) show that the answer is sqrt(x)=4.

You can disagree with it but GMAT says that square root will only take positive value. So sqrt(16) = 4 only.

I think sqrt(16) results in a positive number - so sqrt(16) = 4, not -4. However, when x^2 = 16, then you can have 2 values of x: 4 and -4.

Yep, GMAT considers positive square root only. A should be the correct answer.

Can someone substantiate this one. I mean is it written in the OG somewhr??

For me the answer has to be C

I do not bring my OG with me now, but in Manhattan GMAT prep "Number Properities", it says "Unlike even exponents, which yeilld both a positive and a negative solution, square roots have only one solution. Ex: sqrt(4) = 2. While it is true that (-2)(-2) = 4, the GMAT follows the standard convention that a radical (root) sign denotes only the non-negative root of a number. Thus, 2 is the only solution for sqrt(4)."

Wow, thanks nganle. As much as that surprises me it's good to know! Although I will undoubtedly forget come test time thanks to too many years of brain-programming...

I do not bring my OG with me now, but in Manhattan GMAT prep "Number Properities", it says "Unlike even exponents, which yeilld both a positive and a negative solution, square roots have only one solution. Ex: sqrt(4) = 2. While it is true that (-2)(-2) = 4, the GMAT follows the standard convention that a radical (root) sign denotes only the non-negative root of a number. Thus, 2 is the only solution for sqrt(4)."

with this explanation, I will straightly go to A as my answer