Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If x is an integer, what is the value of x? (3) [#permalink]
17 Nov 2008, 14:41

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