Simple yet tough DS question

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Auzbee: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Mon Jul 09, 2007 6:54 pm; Location: US of A

by Auzbee » Fri Dec 28, 2007 2:54 pm

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.

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Source: Beat The GMAT — Data Sufficiency | Fri Dec 28, 2007 2:54 pm

StarDust845: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Dec 03, 2007 8:32 am; Thanked: 7 times

by StarDust845 » Fri Dec 28, 2007 3:18 pm

Is the answer E?

Calista.

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Auzbee: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Mon Jul 09, 2007 6:54 pm; Location: US of A

by Auzbee » Fri Dec 28, 2007 3:24 pm

Check your inbox.

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StarDust845: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Dec 03, 2007 8:32 am; Thanked: 7 times

by StarDust845 » Fri Dec 28, 2007 3:57 pm

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

Thanks,
Calista.

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joefreddy: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Sat Aug 04, 2007 2:58 am

by joefreddy » Fri Dec 28, 2007 7:35 pm

I think the answer is C.

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beingAndNothing: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Fri Sep 14, 2007 10:35 am; Thanked: 1 times

by beingAndNothing » Fri Dec 28, 2007 8:41 pm

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).

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Auzbee: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Mon Jul 09, 2007 6:54 pm; Location: US of A

by Auzbee » Fri Dec 28, 2007 9:31 pm

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.

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StarDust845: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Dec 03, 2007 8:32 am; Thanked: 7 times

by StarDust845 » Sat Dec 29, 2007 7:18 am

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.

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