Hello WTP,
I'm not sure what you mean by different solutions, but here is my attempt to solve the problem. It took approximately 2 minutes & 4 seconds.
QUESTION
Is ad > bc?
This is a Yes/No question.
STATEMENT 1
a/b > c/d
- If both b and d are positive, then we can cross multiply to get ad > bc, which would answer the question "Yes."
- If both b and d are negative, then we can again cross multiply to get ad > bc, leading to "Yes" again:
a/b(-) > c/d(-)
= a < bc(-)/d(-)
= ad(-) > bc(-)
Which is the same as ad > bc.
- If either b or d is negative, then we will have an answer of "No" :
a/b(-) > c/d(+)
= a < bc(-)/d(+)
= ad(+) < bc(-)
INSUFFICIENT.
STATEMENT 2
b/d > 0
This statement says that both b and d have the same sign, which in and of itself is insufficient to answer the question because there is no information about a and c.
INSUFFICIENT.
STATEMENTS 1 & 2
Looking over the work from STATEMENT 1, we can see that if b and d both have the same sign, then we get the same answer for the posed question, "Yes, ad > bc."
[spoiler]SUFFICIENT. The answer is C, I hope![/spoiler]
Hope this helps!
--Rishi
