m ,r, x, y

bluementor wrote:I believe there is a typo in the question. I've assumed it to be the portion in red:

Baldini wrote: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 x to r
2. The ratio of m + x to r + y is equal to the ratio of x to y

Is m:r = x:y?

Statement 1: If m = x and y = r, then the m:r = x:y
but if m = 6, y=3, x=4 and r=2, then m:r is not equal to x:y. Not sufficient.

Statement 2: The ratio (m+x) : (r+y) will never be equal to m:r because both x and y are nonzero. Therefore m:r is never equal to x:y. Sufficient.

Choose B.

-BM-

Statement 2 is actually sufficient to give a 'yes' answer, not a 'no' answer. Just to give a numerical example to demonstrate that (m+x) : (r+y) can be equal to m:r, if you choose any values of x and y that are in the same ratio as m and r, you'll find an example that makes these equal. Take, say:

m = 4
r = 5
x = 8
y = 10

Then (m+x)/(r+y) = 12/15 = 4/5, and m/r = 4/5.

Back to the question:

Ratios are fractions; the question is asking whether

m/r = x/y

is true. We can rephrase the question by cross-multiplying: is my = xr?

From Statement 1,

m/y = x/r
mr = xy

from which there's no way to conclude that my = xr. This certainly could be true (if, say, all the values were 1), but doesn't need to be (if say, m and y are equal to 10 and x and r are equal to 1).

From Statement 2,

(m+x)/(r+y) = x/y
my + xy = rx + xy
my = rx

which is what we wanted to know. Sufficient.