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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Aug 28, 2016 3:24 am
If m,r,x, and y are positive, is the ratio of m to r equal to the ratio of x to y?

(1) The ratio of m to y is equal to ratio of x to r.
(2) The ratio of m+x to r+y is equal to the ratio of x to y.
Does m/r = x/y?
We can rephrase the question stem by cross-multiplying:
Does my = rx?

Statement 1: m/y = r/x.
Cross-multiplying, we get:
mx = ry.
If m=x=r=y=1, then my = rx.
If m=2, x=1, and r=1, y=2, then my ≠ rx.
INSUFFICIENT.

Statement 2: (m+x)/(r+y) = x/y.
Cross-multiplying, we get:
y(m+x) = x(r+y)
my + xy = rx + xy
my = rx.
SUFFICIENT.

The correct answer is B.
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by Brent@GMATPrepNow » Sun Aug 28, 2016 5:30 am

If m, r, x and y are positive, is the ratio of m to r equal to the ratio of x to y?

(1)the ratio of m to y is equal to the ratio of x to r.
(2)the ratio of m+x to r+y is equal to the ratio of x to y.


We can rephrase the target question as . . .
REPHRASED target question: Does m/r = x/y?

We may find it useful to take the equation m/r = x/y and cross-multiply to get my = rx. This allows us to rephrase the target question in one more way . . .
RE-REPHRASED target question: Does my = rx?

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: The ratio of m to y is equal to ratio of x to r
In other words, m/y = x/r
This LOOKS similar to m/r = x/y (one of our target questions), but it is not the same.
There are several values of m, r, x and y that satisfy this condition. Here are two:
Case a: m = r = x = y = 1, in which case m/r = x/y
Case b: m = 1, y = 2, x = 3 and r = 6, in which case m/r ≠ x/y
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The ratio of m+x to r+y is equal to the ratio of x to y.
In other words, (m+x)/(r+y) = x/y
Cross multiply to get: y(m+x) = x(r+y)
Expand: ym + yx = xr + xy
Subtract xy from both sides to get: ym = xy
Perfect, we've shown that ym = xy, and this is one of our REPHRASED target questions.
Since we can answer the RE-REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

For even more information on rephrasing the target question, you can read this article I wrote for BTG: https://www.beatthegmat.com/mba/2014/06/ ... t-question
Brent Hanneson - Creator of GMATPrepNow.com
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