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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)
Brother Karamazov
Re: If ab > cd and a, b, c and d are all greater than zero   [#permalink] 31 Oct 2012, 14:12
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