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# M26-34

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Math Expert
Joined: 02 Sep 2009
Posts: 49300

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16 Sep 2014, 01:26
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Difficulty:

55% (hard)

Question Stats:

55% (00:55) correct 45% (01:00) wrong based on 196 sessions

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If $$x$$ is a positive integer, is $$\sqrt{x}$$ an integer?

(1) $$\sqrt{7*x}$$ is an integer

(2) $$\sqrt{9*x}$$ is not an integer

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Joined: 02 Sep 2009
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16 Sep 2014, 01:26
Official Solution:

Must know for the GMAT: if $$x$$ is a positive integer then $$\sqrt{x}$$ is either a positive integer or an irrational number. (It cannot be some reduced fraction e.g. $$\frac{7}{3}$$ or $$\frac{1}{2}$$).

Also, note that the question basically asks whether $$x$$ is a perfect square.

(1) $$\sqrt{7*x}$$ is an integer. This statement tells that $$x$$ cannot be a perfect square, because if it is, for example if $$x=n^2$$ for some positive integer $$n$$, then $$\sqrt{7x}=\sqrt{7n^2}=n\sqrt{7} \ne integer$$. Sufficient.

(2) $$\sqrt{9*x}$$ is not an integer. Simplify: $$\sqrt{9*x}=3*\sqrt{x} \ne integer$$, which means that $$\sqrt{x} \ne integer$$. Sufficient.

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07 Nov 2016, 10:32
Statement 1: x is squareroot of an odd power of 7, so not an integer. Sufficient.
Statement 2: x is not a perfect square, hence its square root will not be an integer. Sufficient.
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Joined: 04 Dec 2014
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03 Sep 2018, 07:20
Statement 1: x needs to have odd number of 7 for \sqrt{7x} to be an integer. Hence \sqrt{x} cannot be an integer. Sufficient
Statement 2: Simplify to 3*\sqrt{x}. For this to be a non-integer, \sqrt{x} cannot be an integer. Sufficient
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Joined: 17 Jun 2018
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08 Sep 2018, 22:47
Bunuel chetan2u
I am new to this community.I an unable to find options for answering these questions.Can you guide me.
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Joined: 02 Sep 2009
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09 Sep 2018, 01:53
1
arpitkansal wrote:
Bunuel chetan2u
I am new to this community.I an unable to find options for answering these questions.Can you guide me.

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following posts:
ALL YOU NEED FOR QUANT.

Hope this helps.
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09 Sep 2018, 02:14
Bunuel
thankyou.

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Re: M26-34 &nbs [#permalink] 09 Sep 2018, 02:14
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# M26-34

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