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# M17-35

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:02
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Difficulty:

55% (hard)

Question Stats:

67% (01:32) correct 33% (01:55) wrong based on 221 sessions

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The ratio of $$A$$ to $$B$$ is $$\frac{1}{2}$$. If $$A$$ is increased by $$x\%$$ and $$B$$ is decreased by $$\frac{x}{2}\%$$, which of the following represents the new value of the ratio of $$A$$ to $$B$$?

A. $$\frac{100 + x}{200 - x}$$
B. $$\frac{1 + \frac{x}{100}}{1 - \frac{x}{200}}$$
C. $$\frac{x + 1}{2x + 2}$$
D. $$\frac{2x + 1}{200 - x}$$
E. $$\frac{200 + x}{1 - x}$$

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Joined: 02 Sep 2009
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16 Sep 2014, 00:02
Official Solution:

The ratio of $$A$$ to $$B$$ is $$\frac{1}{2}$$. If $$A$$ is increased by $$x\%$$ and $$B$$ is decreased by $$\frac{x}{2}\%$$, which of the following represents the new value of the ratio of $$A$$ to $$B$$?

A. $$\frac{100 + x}{200 - x}$$
B. $$\frac{1 + \frac{x}{100}}{1 - \frac{x}{200}}$$
C. $$\frac{x + 1}{2x + 2}$$
D. $$\frac{2x + 1}{200 - x}$$
E. $$\frac{200 + x}{1 - x}$$

The new ratio = $$\frac{1 + \frac{x}{100}}{2(1 - \frac{x}{200})} = \frac{1 + \frac{x}{100}}{2 - \frac{x}{100}} = \frac{100 + x}{200 - x}$$.

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Location: United States
GMAT 1: 720 Q50 V38
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09 Feb 2016, 17:32
Alternate approach :

Let A and B be 100 and 200. Ratio 1:2. Now think, x% of 100 is actually x/2% of 200. 10% of 100 ( which is 10 in this case) is 5% of 200. So, basically we are adding and subtracting the same amount from numerator and denominator. Option A does exactly that (100+x)/(200-x).

Manager
Joined: 26 Feb 2018
Posts: 53
Location: India
GMAT 1: 560 Q41 V27
WE: Web Development (Computer Software)

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19 Jun 2018, 12:17
I think this is a high-quality question and I agree with explanation.
Director
Joined: 11 Feb 2015
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22 Oct 2018, 23:10
Let A be Z and B be 2Z. Since Z is appearing in numerator and denominator after increasing the numberator by x% and decreasing by $$\frac{x}{2}$$% therefore z will cancel out.

The remaining workings remain same as aforesaid!
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M17-35   [#permalink] 22 Oct 2018, 23:10
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# M17-35

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