Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Oct 2014, 00:27

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M16 q 34

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Manager
Manager
avatar
Joined: 13 May 2010
Posts: 124
Followers: 0

Kudos [?]: 6 [0], given: 4

M16 q 34 [#permalink] New post 26 Jul 2012, 05:02
If a , b , c , and d are non-zero numbers such that \frac{a}{b} = \frac{c}{d} and \frac{a}{d} = \frac{b}{c} , which of the following must be true?

|a| = |c|
|b| = |d|
|a| = |d|
|b| = |a|
|b| = |c|

Because \frac{a}{b} = \frac{c}{d} , it is true that ad = bc or c = a*\frac{d}{b} . Because \frac{a}{d} = \frac{b}{c} , it is true that ac = bd or c = b*\frac{d}{a} . Thus, c = a*\frac{d}{b} = b*\frac{d}{a} . Because d is not 0, \frac{a}{b} = \frac{b}{a} or a^2 = b^2 or |a| = |b| . To see that the other choices are not necessarily true consider a = 1 , b = -1 , c = -2 , d = 2 .
The correct answer is D.

Can someone please explain me how to solve this problem efficiently? I don't understand the approach used in the solution to manipulate the variables? I did some variable manipulations but figured that if you don't do that a certain way you end up with a different answer like Mod(c) = Mod(d) which is not one of the answer choices?
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 73

Kudos [?]: 527 [0], given: 43

Re: M16 q 34 [#permalink] New post 26 Jul 2012, 09:00
teal wrote:
If a , b , c , and d are non-zero numbers such that \frac{a}{b} = \frac{c}{d} and \frac{a}{d} = \frac{b}{c} , which of the following must be true?

|a| = |c|
|b| = |d|
|a| = |d|
|b| = |a|
|b| = |c|

Because \frac{a}{b} = \frac{cb}{dc} , it is true that ad = bc or c = a*\frac{d}{b} . Because \frac{a}{d} = \frac{b}{c} , it is true that ac = bd or c = b*\frac{d}{a} . Thus, c = a*\frac{d}{b} = b*\frac{d}{a} . Because d is not 0, \frac{a}{b} = \frac{b}{a} or a^2 = b^2 or |a| = |b| . To see that the other choices are not necessarily true consider a = 1 , b = -1 , c = -2 , d = 2 .
The correct answer is D.

Can someone please explain me how to solve this problem efficiently? I don't understand the approach used in the solution to manipulate the variables? I did some variable manipulations but figured that if you don't do that a certain way you end up with a different answer like Mod(c) = Mod(d) which is not one of the answer choices?


The four numbers can be any non-zero real numbers. You can also use some basic algebra and manipulate the two proportions. For example:

Multiply side-by-side the two equalities. It is in fact just simple multiplication of two fractions.
You get \frac{a^2}{bd}=\frac{cb}{dc}, from which it follows that a^2=b^2 (after reduction and cross-multiplication).
Now, take the square root of both sides, and get |a|=|b|.

You can do all the manipulation above as all the numbers are non-zero. And don't forget that \sqrt{x^2}=|x|.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Re: M16 q 34   [#permalink] 26 Jul 2012, 09:00
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic M16-34 Bunuel 1 16 Sep 2014, 00:00
1 Experts publish their posts in the topic M16 Q 37 teal 3 26 Jul 2012, 04:49
M16: Q23 maheshsrini 0 23 Nov 2011, 18:46
1 Experts publish their posts in the topic M16 Q18 gurpreetsingh 2 04 Apr 2010, 12:49
23 Experts publish their posts in the topic M16 Q35 PS from GMAT club tests durgesh79 16 14 Aug 2008, 08:25
Display posts from previous: Sort by

M16 q 34

  Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: Bunuel, WoundedTiger



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.