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# If 4 < x < 100, for how many values of x is x/4 square of an integer?

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Intern
Joined: 14 Sep 2016
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If 4 < x < 100, for how many values of x is x/4 square of an integer?  [#permalink]

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25 Jul 2017, 23:33
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45% (medium)

Question Stats:

74% (00:57) correct 26% (00:40) wrong based on 19 sessions

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If 4 < x < 100, for how many values of x is $$\frac{x}{4}$$ square of an integer?

A. 2
B. 3
C. 4
D. 5
E. 6

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Math Expert
Joined: 02 Sep 2009
Posts: 55271
If 4 < x < 100, for how many values of x is x/4 square of an integer?  [#permalink]

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25 Jul 2017, 23:41
1
dramamur wrote:
If 4 < x < 100, for how many values of x is $$\frac{x}{4}$$ square of an integer?

A. 2
B. 3
C. 4
D. 5
E. 6

$$4 < x < 100$$;

$$1<\frac{x}{4}<25$$ (just divide all parts of the inequality by 4).

$$\frac{x}{4}$$ should be the square of an integer, thus $$\frac{x}{4}$$ could be 2^2 = 4, 3^2 = 9 or 4^2 = 16 (x could be 16, 36, or 64, respectively).

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Re: If 4 < x < 100, for how many values of x is x/4 square of an integer?  [#permalink]

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25 Jul 2017, 23:42
1
Bunuel wrote:
dramamur wrote:
If 4 < x < 100, for how many values of x is $$\frac{x}{4}$$ square of an integer?

A. 2
B. 3
C. 4
D. 5
E. 6

$$4 < x < 100$$;

$$1<\frac{x}{4}<25$$ (just divide all parts of the inequality by 4).

$$\frac{x}{4}$$ should be the square of an integer, thus $$\frac{x}{4}$$ could be 2^2 = 4, 3^2 = 9 or 4^2 = 16 (x could be 16, 36, or 64, respectively).

Similar question from OG: https://gmatclub.com/forum/if-3-x-100-f ... 44069.html
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If 4 < x < 100, for how many values of x is x/4 square of an integer?  [#permalink]

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26 Jul 2017, 18:49
dramamur wrote:
If 4 < x < 100, for how many values of x is $$\frac{x}{4}$$ square of an integer?

A. 2
B. 3
C. 4
D. 5
E. 6

$$4 < x < 100$$

Squares between $$4$$ and $$100$$ are $$= 9, 16, 25, 36, 49, 64, 81$$

Out of the above numbers, numbers that are divisible by $$4 = 16, 36, 64$$

Therefore $$x$$ could be $$= 16, 36, 64$$

Checking $$\frac{x}{4}$$ is square;

$$\frac{16}{4} = 4 ------ (2^2)$$

$$\frac{36}{4} = 9 ------ (3^2)$$

$$\frac{64}{4} = 16 ------ (4^2)$$

Hence total number of values of $$x$$ where $$\frac{x}{4}$$ is square of an integer $$= 3$$

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
If 4 < x < 100, for how many values of x is x/4 square of an integer?   [#permalink] 26 Jul 2017, 18:49
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