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

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New post 25 Jul 2017, 23:33
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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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If 4 < x < 100, for how many values of x is x/4 square of an integer?  [#permalink]

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New post 25 Jul 2017, 23:41
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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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New post 25 Jul 2017, 23:42
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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).

Answer: B.


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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New post 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 \(= 3\)

Answer (B)...

--== 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.
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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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