arjunshn wrote:If p, q, r, and s are non-zero numbers, is pr/qs > r/q?
1) p > s
2) rq > 0
Another way to solve this question is to first rewrite the target question ("
Is pr/qs > r/q?")
First, we can write pr/qs as (r/q)(p/s) to get ("
Is (r/q)(p/s) > r/q?")
Now let's subtract r/q from both sides to get ("
Is (r/q)(p/s) - (r/q) > 0?")
Finally, if we factor out the r/q, we get ("Is
(r/q)[(p/s) - 1] > 0?")
Since we have now written the target question as the product of
(r/q) and
[(p/s) - 1], we can see that the only way to answer the target question is to determine whether
(r/q) is positive or negative
AND to determine whether
[(p/s) - 1] is positive or negative
Now we can examine our statements
Statement 1
No information about
(r/q), so statement 1 is not sufficient
Statement 2
No information about
[(p/s) - 1], so statement 2 is not sufficient
Statements 1 and 2 combined
From statement 2: If rq > 0, then r and q are both positive or both negative, which means
(r/q) must be positive
From statement 1: If p > s, then
[(p/s) - 1] can be either positive or negative
(Proof: if p=3 and s=1, then [(p/s) - 1] is positive and if p=1 and s=-2, then [(p/s) - 1] is negative)
Since
[(p/s) - 1] can be either positive or negative, there is now way to determine whether
(r/q)[(p/s) - 1] > 0
So the statements combined are not sufficient, which means the answer is
E
