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# s03#09

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Status: Time to work on the applications
Joined: 18 Nov 2010
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GMAT 1: 720 Q50 V36
s03#09 [#permalink]

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29 May 2011, 11:32
Is p+q > 1/p + 1/q ?

1)p<q<1

2)pq<1

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

OA:
[Reveal] Spoiler:
E

I disagree with OA because of the following.

The equation can be simplified to :
Is p+q > (p+q)/pq?

Consider 2)
Now, if p = -q, then the condition is NOT satisfied. If p not = q, then 2) woulld still mean that the condition is NOT satisfied. That means with 2), the condition is NEVER satisfied, hence 2) is sufficient. That is why I think the answer should be B. Am I missing something?
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Joined: 20 Dec 2010
Posts: 2010
Re: s03#09 [#permalink]

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30 May 2011, 02:26
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This post received
KUDOS
Chetangupta wrote:
Is it possible to simplify the question to Is pq>1? If so, statement 2 should suffice and answer is B.

$$p+q > 1/p + 1/q$$
$$p+q > \frac{p+q}{pq}$$

Divide $$p+q$$ on both sides
$$pq>1$$

The Divide on both sides part is wrong:
If p=0.5, q=-0.5; you would end up dividing by 0.
If p=-1, q=0.5; you are dividing a -ve number; thus the inequality sign "<" will have to be flipped.

Bottomline,
You should not perform cross-multiplication, multiplication, division unless you know the sign of the variable/expression.
*****************************************************************************************

Furthermore,
Substitution, although may be cumbersome, slow, arduous or unintuitive sometimes, is a full proof method for answering Data Sufficiency.

If you can get two contradicting answers to a question by substituting different numbers, taking all the conditions into account, you can be 100% sure that the statement(s) are Not Sufficient. Algebra, on the other hand, may fail sometimes if not thoroughly executed.
********************************************************************************************
_________________
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Joined: 20 Dec 2010
Posts: 2010
Re: s03#09 [#permalink]

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29 May 2011, 13:00
plakhani wrote:
Is p+q > 1/p + 1/q ?

1)p<q<1

2)pq<1

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

OA:
[Reveal] Spoiler:
E

I disagree with OA because of the following.

The equation can be simplified to :
Is p+q > (p+q)/pq?

Consider 2)
Now, if p = -q, then the condition is NOT satisfied. If p not = q, then 2) woulld still mean that the condition is NOT satisfied. That means with 2), the condition is NEVER satisfied, hence 2) is sufficient. That is why I think the answer should be B. Am I missing something?

If you could justify what you are trying to say with some example, it would be great.

However, the OA is correct in my opinion.

1.
p=0.1, q=0.2; p+q=0.3; 1/p+1/q=10+5=15; p+q < 1/p+1/q
p=-0.2, q=-0.1; p+q=-0.3; 1/p+1/q=-5-10=-15; p+q > 1/p+1/q
Not Sufficient.

2.
The above values of p and q satisfy pq<1.
Not Sufficient.

Combined;
Same set of examples.
Not Sufficient.

Ans: "E"
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Joined: 23 Jan 2011
Posts: 127
Re: s03#09 [#permalink]

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30 May 2011, 00:30
Is it possible to simplify the question to Is pq>1? If so, statement 2 should suffice and answer is B.
Re: s03#09   [#permalink] 30 May 2011, 00:30
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# s03#09

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