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# If ab > cd and a, b, c and d are all greater than zero

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Manager
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If ab > cd and a, b, c and d are all greater than zero [#permalink]

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31 Aug 2012, 05:50
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If ab > cd and a, b, c and d are all greater than zero, which of the following CANNOT be true?

A. c > b
B. d > a
C. b/c < d/a
D. a/c > d/b
E. (cd)2 < (ab)2

Could someone explain how to cross multiply such enequalities, what is the general rule?
[Reveal] Spoiler: OA

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Last edited by Bunuel on 31 Aug 2012, 06:01, edited 1 time in total.
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Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]

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31 Aug 2012, 06:01
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ziko wrote:
If ab > cd and a, b, c and d are all greater than zero, which of the following CANNOT be true?

A. c > b
B. d > a
C. b/c < d/a
D. a/c > d/b
E. (cd)2 < (ab)2

Could someone explain how to cross multiply such enequalities, what is the general rule?

When you multiply/divide both parts of an inequality by a positive value you should keep the sign.
When you multiply/divide both parts of an inequality by a negative value you should flip the sign.

Now, if we multiply both parts of the given inequality by 1/(ac) (which according to the stem must be positive), then we'll get: b/c>d/a, so option C which says that b/c < d/a cannot be true.

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Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]

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24 Sep 2012, 22:03
Hi All,

Is there a way to verify the validity of options a and b. If answer c was also a valid inequality, how could we have verified the first two options?

any inputs on this anyone? Thanks in advance.
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Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]

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31 Oct 2012, 15:12
ab > cd
ab/abcd > cd/abcd
1/cd > 1/ab
cd < ab ==> d/a < b/c (b/c CANNOT BE < d/a)
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Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]

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13 Feb 2015, 14:45
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Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]

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13 Feb 2015, 19:48
Hi All,

This question can be solved by TESTing VALUES. Since there are so many variables, and the answers look a "little crazy", the key is to keep your numbers small and simple.

We're told that (A)(B) > (C)(D) and that A, B, C and D are all POSITIVE. We're asked which of the following CANNOT be true. If we can prove that an answer COULD be true, even once, then we can eliminate it.

Let's TEST VALUES:
Starting with Answer A, is there a way for C to be > B?

IF....
A = 3
B = 2
C = 3
D = 1
Here, C is greater than B. Eliminate Answer A.

We can ALSO eliminate a couple of other answers with this example:
Answer D (3/3 > 1/2) and Answer E (3^2 < 6^2) can be eliminated TOO.

With 2 answers remaining, I'm going to deal with the easier-looking option:

With Answer B, is there a way for D to be > A?

IF...
A = 3
B = 2
C = 1
D = 4
Here, D is greater than A. Eliminate Answer B.

The final answer is the only one left....

[Reveal] Spoiler:
C

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 26 Jun 2012 Posts: 6 Re: If ab > cd and a, b, c and d are all greater than zero [#permalink] ### Show Tags 14 Nov 2015, 19:28 if you take a=3 b=4 c=2 d=1 even option c will be true 3*4>2*1 and b/c>d/a 4/2>1/3 so even option C is true Can you correct me if i am wrong. Some thing wrong in this question EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9279 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: If ab > cd and a, b, c and d are all greater than zero [#permalink] ### Show Tags 14 Nov 2015, 21:27 Hi ashokingmat, If you compare your work to Answer C in the original prompt, you'll notice that you've used the WRONG inequality. Answer C: B/C < D/A You wrote it as B/C > D/A. Your example is a good one though (it does prove that C is not true), you just made a little mistake in your work. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]

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20 Jun 2017, 18:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: If ab > cd and a, b, c and d are all greater than zero   [#permalink] 20 Jun 2017, 18:08
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# If ab > cd and a, b, c and d are all greater than zero

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