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

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If ab > cd and a, b, c and d are all greater than zero [#permalink] New post 31 Aug 2012, 04:50
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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, 05:01, 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] New post 31 Aug 2012, 05:01
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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.

Answer: C.
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Re: If ab > cd and a, b, c and d are all greater than zero [#permalink] New post 24 Sep 2012, 21:03
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] New post 31 Oct 2012, 14:12
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] New post 13 Feb 2015, 13:45
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Re: If ab > cd and a, b, c and d are all greater than zero [#permalink] New post 13 Feb 2015, 18:48
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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....

Final Answer:
[Reveal] Spoiler:
C


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Re: If ab > cd and a, b, c and d are all greater than zero   [#permalink] 13 Feb 2015, 18:48
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