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Rythm09
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Need help solving this problem 25 Sep 2020, 07:06
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If pq ≠ 0, is p2q > pq2 ?

(1) pq < 0

(2) p < 0


For this question , I picked Choice #2- Statement II is sufficient. However , the correct answer is Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

The explanation of the solution was that in st #2 , there is no information given about q.

My logic was - if p<0 , regardless of whether q<0 or q>0 , p2q > pq2 satisfies. So even when we dont know q we can still justify the equation right ?

Please explain.

Thanks

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Need help solving this problem Updated on: 25 Sep 2020, 08:12
Originally posted by ArunSharma12 on 25 Sep 2020, 07:19.
Last edited by ArunSharma12 on 25 Sep 2020, 08:12, edited 1 time in total.
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Quote:

If pq ≠ 0, is p2q > pq2 ?

(1) pq < 0

(2) p < 0
Show more

Given: \(pq ≠ 0\)
\(p^2q > pq^2\)
is \(pq (p - q) > 0\)?

statement 1: pq < 0
but we don't know whether (p - q) > 0.
not sufficient

statement 2: p < 0; implies pq < 0
we have no information on q, so we can not decide the sign of (p - q).
q can be positive or negative or greater than or less than p.
not sufficient

combining both statements,
pq < 0 & p < 0; implies q > 0
so (p - q) is also negative.
we can infer that \(pq(p - q) > 0\)
Ans: C
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Need help solving this problem 25 Sep 2020, 07:26
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Great , Thanks a lot.

I was trying with substituting values . For p = -2 & q=3 or -3 , it did satisfy the equation however for other numbers like p=-5&q=-4 or 4 , it didnt.

Some learning here ..:) . Thank you again.
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ArunSharma12

statement 2: p < 0; implies pq < 0
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I'm not precisely sure what you meant to write here, but when we know "p < 0" is true, we can't conclude that "pq < 0" is true without information about q.

There are a few ways one could approach the question - getting zero on one side in the question, then factoring, lets us see what kind of information we're looking for, for example. I'd say that's the most standard approach to take, and is the most flexible, so it's probably the best one to study, but Arun has posted a solution using that approach above, so I'll offer an alternative:

Is (p^2)(q) > (p)(q^2) ?
1. pq < 0
2. p < 0

When we use Statement 1 alone, we can rephrase the question, by dividing by pq on both sides. Since pq is negative, we'll need to reverse the inequality when we do that. So when Statement 1 is true, our question becomes equivalent to "Is p < q?" Since we don't know if that's true, Statement 1 is not sufficient.

Similarly, using Statement 2 alone, we can rephrase the question by dividing by p on both sides, reversing the inequality when we do. The question then becomes "Is pq < q^2?" Again, we don't know if that's true -- it clearly can be, when q is positive (then the left side is negative, the right side positive) but it can be false if, say, p = -2 and q = -1.

Using both Statements, we know, from the above discussion of Statement 2, that our question becomes "Is pq < q^2?" If pq is negative, from Statement 1, the answer to this question must be yes, because q^2 is positive. So the answer is C.
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Need help solving this problem 25 Sep 2020, 08:21
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IanStewart
ArunSharma12

statement 2: p < 0; implies pq < 0

I'm not precisely sure what you meant to write here, but when we know "p < 0" is true, we can't conclude that "pq < 0" is true without information about q.

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Thanks Ian.
Now that I see my solution, I am not sure how did I conclude pq <0. I probably mixed both statements and made a logical error :-P.

Arun
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Need help solving this problem 25 Sep 2020, 09:10
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Rythm09
If pq ≠ 0, is p2q > pq2 ?

(1) pq < 0

(2) p < 0


For this question , I picked Choice #2- Statement II is sufficient. However , the correct answer is Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

The explanation of the solution was that in st #2 , there is no information given about q.

My logic was - if p<0 , regardless of whether q<0 or q>0 , p2q > pq2 satisfies. So even when we dont know q we can still justify the equation right ?

Please explain.

Thanks
Show more

This question is discussed here: is-p-2q-pq-2-1-pq-0-2-p-153912.html. Hope it helps.

Also, please read carefully and follow our posting rules: rules-for-posting-please-read-this-before-posting-133935.html Thank you.

THIS TOPIC IS LOCKED AND ARCHIVED.

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