Simple yet tough DS question

[Auzbee]

If p < q and p < r, is (p)(q)(r) < p?

(1) pq < 0

(2) pr < 0

I will post the Original answer in a day or two.

[StarDust845]

Is the answer E?

Calista.

[Auzbee]

Check your inbox.

[StarDust845]

Ok I sent the explanation. The formatting is somehow screwing me. So check only my last mail in your inbox.

Thanks,
Calista.

[joefreddy]

I think the answer is C.

[beingAndNothing]

The ineq. can be written as

p(qr-1) < 0

So either 'p<0> 1' or 'p>0 and qr<1>1.

So I think the answer should be (E).

[Auzbee]

Here's the solution to the question. The correct answer is E and StarDust has a beautiful and concise explanation. I also like his trick of using '-b' for negative numbers.

If p < q and p < r, is (p)(q)(r) < p?
(1) pq < 0
(2) pr <0> 0.

Now the question really becomes Is -bqr > -b? where b, q, r are > 0.

Is bqr < b ?
Is qr < 1 ?

Well who knows? qr can be less then 1 or greater than 1. For e.g. if q = r = 1/4 or q = r = 4. We have two different answers.Hope this is clear enough.

Calista.

For some weird reason the complete explanation is getting truncated.

[StarDust845]

Here is the complete solution that I sent Auzbee yesterday.

Stmt (1) implies p < 0 and q > 0, but nothing about r hence INSUFF.
Stmt (2) implies p < 0 and r > 0, but nothing about q hence INSUFF.

Combining both implies p < 0, q and r are positive.

Let's put p = -b where b > 0. (This is a good way to get rid of problems in analysis withj negative numbers).

Now the question really becomes Is -bqr > -b? where b, q, r are > 0.

Is bqr < b ?
Is qr < 1 ?

Well who knows? qr can be less then 1 or greater than 1. For e.g. if q = r = 1/4 or q = r = 4. We have two different answers.Hope this is clear enough.

Hence E.

Calista.