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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

If x/y = c/d and d/c = b/a, which of the following must be true?

I. y/x = b/a II. x/a = y/b III. y/a = x/b

(A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III

d/c = b/a implies c/d=a/b. Together with x/y = c/d --> x/y = c/d = a/b. So y/x= b/a(I is correct). By x/y = a/b --> bx=ay --> x/a = y/b(II is correct and III is not correct). The answer is, therefore, C.
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Re: If x/y = c/d and d/c = b/a, which of the following must be true? [#permalink]

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10 Mar 2016, 03:02

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Substituting numbers for x,y,c,d,b and a is also a viable option.

Considering that \(\frac{x}{y} = \frac{c}{d}\) \(, \frac{c}{d}\) is a multiple of \(\frac{x}{y.}\) Moreover, considering that \(\frac{d}{c} = \frac{b}{a}\), \(\frac{d}{c}\) is a multiple of \(\frac{b}{a}\) but also the reciprocal of \(\frac{x}{y}\).

So, let's consider the following: \(\frac{x}{y}\) = \(\frac{4}{2}\) = \(\frac{c}{d}\)= \(\frac{8}{4}\) then \(\frac{d}{c}\) = \(\frac{4}{8}\) = \(\frac{b}{a}\)= \(\frac{8}{16}\).

I. y/x = b/a 2/4 = 8/16 --> 2/4 is a multiple of 8/16 therefore TRUE II. x/a = y/b 4/16 = 2/8 --> 4/16 is a multiple of 2/8 therefore TRUE III. y/a = x/b 2/16 does not equal 4/8 therefore NOT TRUE.

NOW, PLUG IN #S FOR VARIABLES: > y=24, x=2, d=36, c=3, b=48, a=4 >> plug these into the *REPHRASED* above. don't you clearly see how each of these gives you a multiple of 12?