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# M02 Q11 DS

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Intern
Joined: 25 Aug 2008
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27 Aug 2008, 18:06
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Is $$p^2 > q^2$$ ?

1. $$p > 0$$
2. $$q > 0$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

The given statement simplifies to:
$$p^2 - q^2 > 0$$

The real question, then is this: is $$(p + q) (p-q) > 0$$ ? The statements taken together allow for $$p > q$$ and $$p < q$$ , which makes the sign either positive or negative.

I don't understand the answer. Could someone break it down further please?

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27 Aug 2008, 23:40
idleking wrote:
Is $$p^2 > q^2$$ ?

1. $$p > 0$$
2. $$q > 0$$

(C) 2008 GMAT Club - m02#11

The given statement simplifies to:
$$p^2 - q^2 > 0$$

The real question, then is this: is $$(p + q) (p-q) > 0$$ ? The statements taken together allow for $$p > q$$ and $$p < q$$ , which makes the sign either positive or negative.

I don't understand the answer. Could someone break it down further please?

$$p^2 - q^2 > 0$$

1) p>0

p^2 - q^2 ---> +ve when p>q (assume q is also positive)
p^2 - q^2 ---> -ve ve when p<q (assume q is also positive)

two solutions insuffcient

2) q>0

p^2 - q^2 ---> +ve when p>q (assume p is also positive)
p^2 - q^2 ---> -ve when p<q (assume p is also positive)

two solutions insuffcient

combine.
p>0 q>0 AND DON'T know the proper relation between p and q
p>q q>p

p^2 - q^2 --> lead +ve or -ve values depends on p>q or q>p
insuffcient

E.
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Intern
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02 Dec 2009, 12:54
p^2 > q^2 ? can be rephrased as |p| > |q| ?

1. p > 0
Doesn't give any information on relationship between absolute values of p and q

2. q > 0
Doesn't give any information on relationship between absolute values of p and q

1 & 2 Combined also doesn't give any information on the relationship.

Hence E.

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Intern
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03 Dec 2009, 12:26
Yeah I think you're just overthinking it.

In order to know whether $$p^2 > q^2$$ we have to know something about the relationship between p and q -- that one is larger than the other, that one is negative and one is positive, that one is less than 1 and the other isn't, etc.

Neither of the two statements separately nor the two statements combined give you any information about this.

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Intern
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03 Dec 2009, 12:38
Making a little change in question, say:

2. q < 0

The answer would still be E

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Senior Manager
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07 Dec 2009, 18:07
Actually I wouldn't take the pains of factorizing and all that .. keeping it simple

Square of any number is positive .. so unless the answer choices help establishing a relationship between p and q it's impossible to say which is greater. Hence the option E.
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Intern
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09 Dec 2010, 07:01
jeckll wrote:
Yeah I think you're just overthinking it.

In order to know whether $$p^2 > q^2$$ we have to know something about the relationship between p and q -- that one is larger than the other, that one is negative and one is positive, that one is less than 1 and the other isn't, etc.

Neither of the two statements separately nor the two statements combined give you any information about this.

Enough said here. P and Q could be equal in each of the scenarios. No way to tell if they are not, so E

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09 Dec 2010, 07:25
no need to expand the equation
just put values of p and q as fractions.

Posted from my mobile device

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09 Dec 2010, 10:04
idleking wrote:
Is $$p^2 > q^2$$ ?

1. $$p > 0$$
2. $$q > 0$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

The given statement simplifies to:
$$p^2 - q^2 > 0$$

The real question, then is this: is $$(p + q) (p-q) > 0$$ ? The statements taken together allow for $$p > q$$ and $$p < q$$ , which makes the sign either positive or negative.

I don't understand the answer. Could someone break it down further please?

Looking at statement 1) we have information for P but not Q so I eliminated A & D off the bat.
Looking at statement 2) we have information for Q but not for P so I eliminate B as well.

We are only left with C or E. Since P and Q are greater than 0 and there is no mention of integers in the problem I am going to test a low number 1 and a fraction .5

Here is what I have for my table, respectively..

P:1,.5,1,.5
Q:.5,1,1,.5

Putting these numbers in the original question I get the following...
Yes, No, No, No

Cross out C since it is insufficient.

E all the way
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I'm trying to not just answer the problem but to explain how I came up with my answer. If I am incorrect or you have a better method please PM me your thoughts. Thanks!

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09 Dec 2010, 22:09
since each statement alone is insufficient to answer, considering two statements together still not sufficient to answer as we do not whether P or Q is greater. For example : As both P and Q are positives , if P=2,Q=1, then P*P> Q*Q.

if P=1,Q= 2, then P*P<Q*Q. No definite answer, so it is insufficient to answer. answer is E

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10 Dec 2010, 01:14
Dear GOD! Please dont do this to me. I am less than a month away from my test need a load of tough questions to practice with.
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Respect,
Vaibhav

PS: Correct me if I am wrong.

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11 Dec 2010, 22:30
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E.

from question stem it is apparent that sign of variables does not have any impact on the solution
since both p and q are squared its the absolute value that we are after of each variable

Both Statement 1 and 2 provide only the sign of the number, which is postive for both of them.
Hence neither alone nor together are they sufficient to answer the question

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13 Dec 2010, 02:13

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13 Dec 2011, 09:41
I think the best way to go about this is absolute value. Anything squared is the same as taking absolute value. A and B do not help. Putting them together doesn't either. E

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15 Dec 2011, 08:22
Easy questions. Just try with test numbers, you should get the correct answer.

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18 Feb 2012, 15:03
a) even if we have p = pos, q^2 can still be suff or insuff (ie. p = 2, q = 1 or -3)
b) even if we have q = pos, p^2 can still be suff or insuff (ie. q = 2, p = 1 or -3)
d) we've shown both are insuff
c) well we know both are pos, but if you test fractions or integers they can go either way.

E.

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13 Dec 2012, 06:08
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idleking wrote:
Is $$p^2 > q^2$$ ?

1. $$p > 0$$
2. $$q > 0$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

The given statement simplifies to:
$$p^2 - q^2 > 0$$

The real question, then is this: is $$(p + q) (p-q) > 0$$ ? The statements taken together allow for $$p > q$$ and $$p < q$$ , which makes the sign either positive or negative.

I don't understand the answer. Could someone break it down further please?

Is $$p^2 > q^2$$ ?

Is $$p^2 > q^2$$ ? --> is $$|p|>|q|$$? So, the question basically asks whether $$p$$ is further from zero, on a number line, than $$q$$.

(1) $$p > 0$$. Not sufficient since there is no info abut $$q$$.
(2) $$q > 0$$. Not sufficient since there is no info abut $$p$$.

(1)+(2) We know that both $$p$$ and $$q$$ are positive, though we don't know which one is further from zero (we don't know their relative position on a number line). Not sufficient.

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13 Dec 2012, 06:53
We can directly conclude it to be E since we have not been given any relationship between p and q.

Could be tricked by the problem if someone is in a hurry!!!

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13 Dec 2012, 06:56
Since p and q can take the form of a + whole no. or a + fraction.
And any of the numbers can be greater than the other.
Considering p>q and that they are whole nos. will result in different conclusion if they are fractions.

Choice E is the correct ans!

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13 Dec 2012, 07:36
pretty easy one... Got it correct..

Posted from my mobile device
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Re: M02 Q11 DS   [#permalink] 13 Dec 2012, 07:36

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# M02 Q11 DS

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