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Statements (1) and (2) combined are insufficient. Consider \(p = \frac{1}{3}\), \(q = \frac{1}{2}\) (the answer is "no") and \(p = -\frac{1}{2}\), \(q = -\frac{1}{3}\) (the answer is "yes"). We must remember that \(p\) and \(q\) are not necessarily positive.

p+q>1/p+1/q can be re-written as (p+q)pq>(p+q). Cancelling (p+q) on both sides, the question can be re-written as is pq>1?

St II says pq<1 and so St II is sufficient.

1. You cannot multiply both sides by pq because we don't know whether it's positive or negative (if it's negative you should flip the sign). 2. You cannot reduce by p+q by the same reason.

p+q>1/p+1/q can be re-written as (p+q)pq>(p+q). Cancelling (p+q) on both sides, the question can be re-written as is pq>1?

St II says pq<1 and so St II is sufficient.

1. You cannot multiply both sides by pq because we don't know whether it's positive or negative (if it's negative you should flip the sign). 2. You cannot reduce by p+q by the same reason.

In this kind of question is it helpfull to try tu reduce the question stem or is better to try numbers directly to the statements?, for instance I try to reduce and the question stem result in (pq)squared - 1 > 0

p+q>1/p+1/q can be re-written as (p+q)pq>(p+q). Cancelling (p+q) on both sides, the question can be re-written as is pq>1?

St II says pq<1 and so St II is sufficient.

1. You cannot multiply both sides by pq because we don't know whether it's positive or negative (if it's negative you should flip the sign). 2. You cannot reduce by p+q by the same reason.

In this kind of question is it helpfull to try tu reduce the question stem or is better to try numbers directly to the statements?, for instance I try to reduce and the question stem result in (pq)squared - 1 > 0

Thanks a lot.

Regards.

Luis Navarro Looking for 700

First of all if you manipulate with the inequality you don't get (pq)^2 - 1.

Next, it depends on a question and you math skills what approach to choose.

I too worked with the same approach. Additionally i also assumed "what if one of the numbers equaled 0" if that was the case then equation in question statement would have an undefined side RHS with 1/0. Based on that i quickly eliminated. is that the right approach considering nothing is mentioned about both numbers being non-zero?

I too worked with the same approach. Additionally i also assumed "what if one of the numbers equaled 0" if that was the case then equation in question statement would have an undefined side RHS with 1/0. Based on that i quickly eliminated. is that the right approach considering nothing is mentioned about both numbers being non-zero?

It is safe to assume that both P and Q will not be equal to 0 since that if that were the case it would lead to "undefined" results. I think the assumption is to understand that such scenarios don't exist within the bounds of the GMAT Quantitative Reasoning world.
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The answer must be option E. You can have different cases here. Both +ve, both -ve , & one +ve and one -ve. Try out with all the three cases and you will realise that both together are not sufficient.
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