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

ab > cd
ab/abcd > cd/abcd
1/cd > 1/ab
cd < ab ==> d/a < b/c (b/c CANNOT BE < d/a)
Brother Karamazov

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:

GMAT assassins aren't born, they're made,
Rich

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

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

Its C..

I was stuck between B & C only. B can be sometimes true, but C can never be true. Hence, C.

a,b,c,d > 0
ab>cd

A. INCORRECT. Can/Cannot be TRUE: as c can be greater than b or less than b. We can't say which is greater
B. INCORRECT . Can/Cannot be TRUE: Again similar to option A, here also d can be greater than or less than a. We can't say which is greater.
C. CORRECT. Cannot be TRUE: ab>cd -> b/c > d/a. So, b/c < d/a is totally incorrect.
D. INCORRECT. a/c > d/b This is totally possible.
E. INCORRECT. (ab)^2 > (cd)^2. This is also true.

Answer C

We can divide the given inequality by ac since we know that all of our variables are greater than zero:

ab/(ac) > cd/(ac)

b/c > d/a

Since b/c will always be greater than d/a, b/c < d/a can NEVER be true.

Answer: C

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