If x is an integer, what is the value of x? : GMAT Data Sufficiency (DS)
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# If x is an integer, what is the value of x?

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02 Jun 2010, 08:48
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If √x is an integer, what is the value of √x?

(1) 11 < x < 17
(2) 2 < √x < 5
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02 Jun 2010, 17:43
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alokchaks wrote:
(1) The only perfect square in this range is 16. So √x can be +4 or -4. Not Sufficient.
(2) The possible values for √x are 3 and 4. Not sufficient.

Combining (1) and (2), we get √x = 4.
Ans C

Am I missing something?

Square root function cannot give negative result.

Any nonnegative real number has a unique non-negative square root called the principal square root and unless otherwise specified, the square root is generally taken to mean the principal square root.

When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt[4]{x}$$, then the only accepted answer is the positive root.

That is, $$\sqrt{25}=5$$, NOT +5 or -5. In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5. Even roots have only non-negative value on the GMAT.

Odd roots will have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.
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Re: If x is an integer, what is the value of x? [#permalink]

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11 Aug 2016, 08:06
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Hi Bunuel

In statement 2 3 is not a perfect square and ques says sqrt x is an integer. Please clarify
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02 Jun 2010, 10:41
ajitsah wrote:
If √x is an integer, what is the value of √x?

(1) 11 < x < 17
(2) 2 < √x < 5

If $$\sqrt{x}$$ is an integer, what is the value of $$\sqrt{x}$$?

$$\sqrt{x}$$ is an integer means that $$x$$ is a perfect square.

(1) $$11<x<17$$ --> the only perfect square in this range is 16. So $$\sqrt{x}=4$$. Sufficient.

(2) $$2<\sqrt{x}<5$$ --> $$\sqrt{x}$$ can be 3 or 4. Two answers, hence not sufficient.

Hope it's clear.
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02 Jun 2010, 10:59
i: The only perfect square in this range is 16, so $$sqrt x = 4$$; sufficient
ii: $$sqrt x$$ can be 3 or 4. insufficient.

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02 Jun 2010, 17:28
(1) The only perfect square in this range is 16. So √x can be +4 or -4. Not Sufficient.
(2) The possible values for √x are 3 and 4. Not sufficient.

Combining (1) and (2), we get √x = 4.
Ans C

Am I missing something?
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02 Jun 2010, 18:02
Thanks for the explanation. I will embed it in my head.

I've given you a +1 Kudos.
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18 Sep 2014, 05:13
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11 Aug 2016, 09:20
rahulgupta99 wrote:
Hi Bunuel

In statement 2 3 is not a perfect square and ques says sqrt x is an integer. Please clarify

Solution says: $$\sqrt{x}$$ can be 3 or 4, so x is 3^2 or 4^2.
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13 Aug 2016, 06:46
Thanks Bunuel
Re: If x is an integer, what is the value of x?   [#permalink] 13 Aug 2016, 06:46
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