In a certain school, the ratio of boys to girls is 5 to 13. : GMAT Problem Solving (PS)
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# In a certain school, the ratio of boys to girls is 5 to 13.

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Joined: 06 Apr 2012
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In a certain school, the ratio of boys to girls is 5 to 13. [#permalink]

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24 Sep 2012, 03:12
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87% (01:43) correct 13% (00:47) wrong based on 119 sessions

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In a certain school, the ratio of boys to girls is 5 to 13. If there are 72 more girls than boys, how many boys are there?

A. 27
B. 36
C. 45
D. 72
E. 117

[Reveal] Spoiler:
This is a pretty simple problem, however I was looking for purely algebraic way(s) to solve it. For some reason have trouble expressing it properly, please help to set it up.
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Sep 2012, 03:17, edited 1 time in total.
Edited the question.
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Re: In a certain school, the ratio of boys to girls is 5 to 13. [#permalink]

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24 Sep 2012, 03:19
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Expert's post
ikokurin wrote:
This is a pretty simple problem, however I was looking for purely algebraic way(s) to solve it. For some reason have trouble expressing it properly, please help to set it up.

In a certain school, the ratio of boys to girls is 5 to 13. If there are 72 more girls than boys, how many boys are there?
A. 27
B. 36
C. 45
D. 72
E. 117

Given: $$\frac{b}{g}=\frac{5x}{13x}$$, for some positive integer $$x$$. So, the number of boys must be a multiple of 5. Only answer choice C fits.

Alternately you can write: $$5x+72=13x$$ --> $$x=9$$ --> $$boys=5x=5*9=45$$.

Hope it helps.
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Re: In a certain school, the ratio of boys to girls is 5 to 13. [#permalink]

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24 Sep 2012, 11:18
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we know 5/13 and this is also equal to x/x+72. ---> 5x + 360 = 13x ---> x = 45.

Albeit, the Bunuel's approach is even more straight
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Re: In a certain school, the ratio of boys to girls is 5 to 13. [#permalink]

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24 Sep 2012, 13:05
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The ratio of b to G is 5:13 and the other data point is G are more than boys by 72...
Looking at the ratio we can say that the 8(13-5) extra parts caused this diff of 72. so 1 part corresponds to 72/8=9 and so
5 parts correspond to 5*9 = 45.

PS: always double check with the answer if u r using this approach.
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Re: In a certain school, the ratio of boys to girls is 5 to 13.   [#permalink] 24 Sep 2012, 13:05
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# In a certain school, the ratio of boys to girls is 5 to 13.

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