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# The ratio of a numerator to denominator is 2:3. If six is

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Manager
Joined: 04 Jan 2013
Posts: 80
The ratio of a numerator to denominator is 2:3. If six is [#permalink]

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23 Mar 2013, 14:59
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25% (medium)

Question Stats:

78% (02:03) correct 22% (01:23) wrong based on 49 sessions

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The ratio of a numerator to denominator is 2:3. If six is subtracted from the numerator, the new fraction is now 2/3 of the original fraction. Find the numerator.'

A. 9
B. 10
C. 16
D. 7
E. 18
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Mar 2013, 04:35, edited 1 time in total.
Edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 39626
Re: The ratio of a numerator to denominator is 2:3. If six is [#permalink]

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24 Mar 2013, 04:43
chiccufrazer1 wrote:
The ratio of a numerator to denominator is 2:3. If six is subtracted from the numerator, the new fraction is now 2/3 of the original fraction. Find the numerator.'

A. 9
B. 10
C. 16
D. 7
E. 18

The ratio of a numerator to denominator is 2:3 --> $$\frac{x}{y} = \frac{2}{3}$$;

If six is subtracted from the numerator, the new fraction is now 2/3 of the original fraction --> $$\frac{x - 6}{y} = \frac{2}{3}*\frac{2}{3}$$ --> $$\frac{x}{y} -\frac{6}{y} = \frac{4}{9}$$ --> $$\frac{2}{3}-\frac{6}{y} = \frac{4}{9}$$ --> $$\frac{6}{y}=\frac{2}{9}$$ --> $$y=27$$ --> $$\frac{x}{27}=\frac{2}{3}$$ --> $$x=18$$.

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Re: The ratio of a numerator to denominator is 2:3. If six is   [#permalink] 24 Mar 2013, 04:43
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