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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # If x/y = c/d and d/c = b/a, which of the following must be true?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 50578 If x/y = c/d and d/c = b/a, which of the following must be true? [#permalink] ### Show Tags 18 Oct 2015, 11:57 5 10 00:00 Difficulty: 15% (low) Question Stats: 77% (01:12) correct 23% (01:15) wrong based on 1158 sessions ### HideShow timer Statistics 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. _________________ Manager Joined: 11 Sep 2013 Posts: 110 Re: If x/y = c/d and d/c = b/a, which of the following must be true? [#permalink] ### Show Tags 18 Oct 2015, 12:19 3 1 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. 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 Manager Joined: 01 Mar 2015 Posts: 65 Re: If x/y = c/d and d/c = b/a, which of the following must be true? [#permalink] ### Show Tags 18 Oct 2015, 21:12 2 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. 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 VP Status: It's near - I can see. Joined: 13 Apr 2013 Posts: 1282 Location: India Concentration: International Business, Operations GMAT 1: 480 Q38 V22 GPA: 3.01 WE: Engineering (Consulting) Re: If x/y = c/d and d/c = b/a, which of the following must be true? [#permalink] ### Show Tags 19 Oct 2015, 20:56 1 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) _________________ "Do not watch clock; Do what it does. KEEP GOING." Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6504 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x/y = c/d and d/c = b/a, which of the following must be true? [#permalink] ### Show Tags 20 Oct 2015, 01:29 2 2 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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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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20 Oct 2015, 01:45
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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22 Oct 2015, 02:22
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

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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, 02:02
1
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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13 Oct 2017, 15:56
3
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. $$\frac{24}{4}$$ = $$\frac{2}{48}$$

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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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14 Oct 2018, 07:52
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Re: If x/y = c/d and d/c = b/a, which of the following must be true? &nbs [#permalink] 14 Oct 2018, 07:52
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