Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44290

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
1
This post received KUDOS
Expert's post
8
This post was BOOKMARKED
Question Stats:
76% (01:14) correct 24% (01:24) wrong based on 846 sessions
HideShow timer Statistics



Manager
Joined: 11 Sep 2013
Posts: 112

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
1
This post received KUDOS
1
This post was BOOKMARKED
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



Intern
Joined: 01 Mar 2015
Posts: 49

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
1
This post was BOOKMARKED
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



Senior Manager
Joined: 13 Apr 2013
Posts: 345
Location: India
Concentration: International Business, Operations
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, 21:56
1
This post received KUDOS
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)
_________________
"Success is not as glamorous as people tell you. It's a lot of hours spent in the darkness."



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5034
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
1
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
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 oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 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: 65
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: 19

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: 85

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
1
This post received KUDOS
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: 26 Dec 2015
Posts: 285
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
2
This post received KUDOS
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




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






