Data Sufficiency

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

Target question: Is the ratio of m to r is equal to the ratio of x to y?

We can rephrase this 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?

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

bml1105 wrote:If we cross multiple Statement 1 of m/r = x/y, we still get our Re-Rephrased target question of my = xr.

Wouldn't that mean that Case B isn't an option?

Statement 1 doesn't tell us that m/r = x/y
Statement 1 tells us that m/y = x/r

Cheers,
Brent

bml1105 wrote:So the statements need to match both the Rephrased target question AND the Re-rephrased target question? Not just one of them?

You have misinterpreted statement 1. It does NOT say that m/r = x/y.
It says m/y = x/r

Cheers,
Brent