May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55271

If x/y = c/d and d/c = b/a, which of the following must be true?
[#permalink]
Show Tags
18 Oct 2015, 12:57
Question Stats:
77% (01:33) correct 23% (01:55) wrong based on 1273 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.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Senior Manager
Joined: 26 Dec 2015
Posts: 253
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)

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




Manager
Joined: 11 Sep 2013
Posts: 108

Re: If x/y = c/d and d/c = b/a, which of the following must be true?
[#permalink]
Show Tags
18 Oct 2015, 13:19
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: 74

Re: If x/y = c/d and d/c = b/a, which of the following must be true?
[#permalink]
Show Tags
18 Oct 2015, 22:12
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 TrueII. x/a = y/b TrueIII. y/a = x/b not always true answer choice C



SVP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1674
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Real Estate)

Re: If x/y = c/d and d/c = b/a, which of the following must be true?
[#permalink]
Show Tags
19 Oct 2015, 21:56
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: 7372
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, 02:29
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 spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $149 for 3 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Manager
Status: tough ... ? Naaahhh !!!!
Joined: 08 Sep 2015
Posts: 63
Location: India
Concentration: Marketing, Strategy
WE: Marketing (Computer Hardware)

Re: If x/y = c/d and d/c = b/a, which of the following must be true?
[#permalink]
Show Tags
20 Oct 2015, 02:45
x/y = c/d = a/b.
option 1 & 2 are correct. Ans. c



Intern
Joined: 25 Jul 2012
Posts: 16

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



Manager
Joined: 03 Jan 2015
Posts: 72

Re: If x/y = c/d and d/c = b/a, which of the following must be true?
[#permalink]
Show Tags
10 Mar 2016, 03:02
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.



Senior Manager
Joined: 14 Feb 2017
Posts: 277
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26 GMAT 2: 550 Q43 V23 GMAT 3: 650 Q47 V33
GPA: 2.61
WE: Management Consulting (Consulting)

If x/y = c/d and d/c = b/a, which of the following must be true?
[#permalink]
Show Tags
28 Nov 2018, 16:35
LakerFan24 wrote: 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 This is the only approach I was able to follow. Can someone kindly explain to me the OG's solution? They solve for statement ii as follows: ii. since y/x = b/a x*(y/x = b/a) y= xb/a therefore ay = bx thus y/b = x/a I thought we couldn't infer the signs (pos/neg) of variables in questions like this?



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6231
Location: United States (CA)

Re: If x/y = c/d and d/c = b/a, which of the following must be true?
[#permalink]
Show Tags
21 Mar 2019, 17:58
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. We can use some convenient numbers: x = 2, y = 3 c = 4, d = 6 b = 12, a = 8 Now we can analyze each Roman numeral: I. 3/2 = 12/8 ? 3/2 = 3/2 → I is true. II. 2/8 = 3/12 ? 1/4 = 1/4 → II is true. III. 3/8 = 2/12 ? 3/8 ≠ 1/6 → III is not True. Answer: C
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.




Re: If x/y = c/d and d/c = b/a, which of the following must be true?
[#permalink]
21 Mar 2019, 17:58






