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Ratio Problem

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Ratio Problem

by relaxin99 » Wed Feb 04, 2009 8:19 pm
If m, r, x & 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 eual to the ratio of x to y.

With the answer, can you all please explain how you came up with the answer thanks
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Source: — Data Sufficiency |
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by DanaJ » Thu Feb 05, 2009 12:50 am
1 is insufficient because m/x = y/r only tells us that mr = xy. We cannot determine if m/r = x/y from this formula. Let me show you why:
mr = xy | :y^2
mr/(y^2) = x/y | :r^2
m/r *(1/y^2) = x/y *(1/r^2). In order to establish if m/r = x/y, we would need to know if 1/y^2 = 1/r^2, which we do not.

2. is sufficient, since, if (a + c)/(b + d) = c/d, then a/b = c/d. You can prove this by multiplying:
(m+x)/(r+y) = x/y
(m+x)*y = (r+y)*x
my + xy = rx + xy
my = rx and divide this by ry on each side and you get m/r = x/y.

Answer B.
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by relaxin99 » Fri Feb 06, 2009 4:48 pm
Hey Dana, wow great explanation...bravo
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