ds:inequality

[arjunshn]

If p, q, r, and s are non-zero numbers, is pr/qs > r/q?
1) p > s
2) rq > 0

[HSPA]

given (p/s)*(r/q) > (r/q)
=> is p/s > 1

is p and s integers?? are they both negitive or positive

1) P > S .. p = -1 and s = -2 and P/S = 1/2 [not okay]
p = 2 and s = 1 and P/S = 2 > 1 [Okay]
=> insufficient
2) rq>0 is not required here..

IMO E

[Anurag@Gurome]

If p, q, r, and s are non-zero numbers, is pr/qs > r/q?
1) p > s
2) rq > 0

Question is: Is pr/qs > r/q?

(1) If p = 5, s = 4, r = q = 1, then pr/qs = 5/4 = 1.25 > 1. Here, pr/qs > r/q.
If p = -1, s = -2, r = -1, q = -1, then pr/qs = 1/2 = 0.5 < 1. Here pr/qs < r/q.
No unique answer.
So, (1) is NOT SUFFICIENT.

(2) rq > 0 implies either r and q are both positive or both negative. Again taking the examples in statement 1, we don't get a unique answer.
So, (2) is NOT SUFFICIENT.

Combining (1) and (2), also is NOT SUFFICIENT.

The correct answer is E.

[Brent@GMATPrepNow]

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

[MAAJ]

With statement 2 you can also multiple by Q/R because R/Q or Q/R is positive

PR/QS > R/Q ?
PR/QS * (Q/R) > R/Q * (Q/R) ?
PRQ/QSR > 1 ?
P/S > 1 ?

And with statement 1 we can't answer that because P/S is a ratio.