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

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

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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

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[Reveal] Spoiler: OA

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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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New post 18 Oct 2015, 13:19
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Bunuel wrote:
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

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x/y=c/d=a/b

I. y/x = b/a: TRUE
II. x/a = y/b: TRUE
III. y/a = x/b: Only when a=b

Ans: I+II => 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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New post 18 Oct 2015, 22:12
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Bunuel wrote:
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

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Here, y, d, c, and a are in denominator, so we can take them to be non zero and then rest would also be non zero

x/y = c/d and d/c = b/a
\(x/y = c/d = a/b\)

I. y/x = b/a True
II. x/a = y/b True
III. y/a = x/b not always true

answer choice 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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New post 19 Oct 2015, 21:56
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Bunuel wrote:
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

Kudos for a correct solution.


My Solution:

Given, x/y =c/d and d/c=b/a

If d/c=b/a then c/d =a/b, therefore we can say that x/y=a/b or y/x=b/a. Statement I is true

If x/y=a/b, then x/a=y/b. Statement II is true

As x/y=a/b, then y/a = x/b can't be true. So statement III is not true

Answer is Option C (I & II only)

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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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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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New post 20 Oct 2015, 02:45
x/y = c/d = a/b.

option 1 & 2 are correct. Ans. 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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New post 22 Oct 2015, 03:22
Given:

x/y=c/d or we can say: xd=cy or d/c=y/x --- 1

Given:

d/c=b/a --- 2

From 1 and 2, d/c=y/x=b/a

so we can say: y/x=b/a AND y/b=x/a

Answer is 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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New post 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.

Only I and II are true. The correct answer is 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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New post 13 Oct 2017, 16:56
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You can solve this by plugging in #s (see below):


QUESTION: \(\frac{x}{y}\) = \(\frac{c}{d}\) and \(\frac{d}{c}\) = \(\frac{b}{a}\)

** REPHRASED: \(\frac{y}{x}\) = \(\frac{d}{c}\) = \(\frac{b}{a}\)

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?


I. \(\frac{24}{2}\) = \(\frac{48}{4}\)

II. \(\frac{2}{4}\) = \(\frac{24}{48}\)

III. \(\frac{24}{4}\) = \(\frac{2}{48}\)

Kudos please if you find this helpful :)

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Re: If x/y = c/d and d/c = b/a, which of the following must be true?   [#permalink] 13 Oct 2017, 16:56
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