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# If 8 < m < 120, how many integer m are possible for m/3 is a square

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Intern
Joined: 09 Feb 2011
Posts: 15
If 8 < m < 120, how many integer m are possible for m/3 is a square  [#permalink]

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09 Feb 2011, 16:30
2
2
00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:43) correct 46% (02:05) wrong based on 62 sessions

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If 8 < m < 120, how many integer m are possible for m/3 is a square of integer?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Math Expert
Joined: 02 Sep 2009
Posts: 52392
Re: If 8 < m < 120, how many integer m are possible for m/3 is a square  [#permalink]

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09 Feb 2011, 16:50
loveparis wrote:
83. If 8 < m < 120, how many integer m are possible for m/3 is a square of integer?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Given: $$\frac{m}{3}=n^2$$ --> $$m=3n^2$$, for some integer $$n$$ and $$8<m<120$$. So, $$8<3n^2<120$$ --> $$\frac{8}{3}<n^2<40$$ --> there are total of 5 perfect square between 2.6 and 40: 4, 9, 16, 25, and 36 (so m could be: 12, 27, 48, 75, or 108).

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Re: If 8 < m < 120, how many integer m are possible for m/3 is a square  [#permalink]

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30 Mar 2017, 04:13
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Re: If 8 < m < 120, how many integer m are possible for m/3 is a square &nbs [#permalink] 30 Mar 2017, 04:13
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