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We don't need R at all, so substitute it. The question becomes is \(\frac{P}{Q}\leq{P}\)? Notice that we can not reduce both sides by P since we don't know the sign of it, thus don't know whether we should flip the sign of the inequality when reducing.

(1) P>50 --> P is positive - reduce by it. The question becomes is \(\frac{1}{Q}\leq{1}\)? --> is \(Q<0\) or \(Q\geq{1}\)? We don't know that. Not sufficient.

(2) 0<Q≤20. No info about P. Not sufficient.

(1)+(2) From (1) the question became: is \(Q<0\) or \(Q\geq{1}\)? Now, (2) says \(0<Q\leq{20}\), which is not sufficient to answer the question definitely: if \(1\leq{Q}\leq{20}\) the answer is YES but if \(0<Q<1\) the answer is NO. Not sufficient.

doesn't combining (1)+(2) imply 1<=q<=2, common region implied by options (1) and (2)

From (1) the question became: is \(\frac{1}{Q}\leq{1}\)? (2) says \(0<Q\leq{20}\). Now, if \(1\leq{Q}\leq{20}\) (for example if \(Q=2\)) the answer is YES but if \(0<Q<1\) (for example if \(Q=\frac{1}{2}\)) the answer is NO. Not sufficient.

First of all a proper GMAT question would mention that Q doesn't equal to zero (as it's in denominator).

Next, we don't need R at all, substitute it. The question becomes is \(\frac{P}{Q}\leq{P}\)? Notice that we can not reduce both sides by P since we don't know the sign of it, thus don't know whether we should flip the sign of the inequality when reducing.

(1) P>50 --> P is positive - reduce by it. The question becomes is \(\frac{1}{Q}\leq{1}\)? --> is \(Q<0\) or \(Q\geq{1}\)? We don't know that. Not sufficient.

(2) 0<Q≤20. No info about P. Not sufficient.

(1)+(2) From (1) the question became: is \(Q<0\) or \(Q\geq{1}\)? Now, (2) says \(0<Q\leq{20}\), which is not sufficient to answer the question definitely: if \(1\leq{Q}\leq{20}\) the answer is YES but if \(0<Q<1\) the answer is NO. Not sufficient.

Answer: E.

Hope it's clear.

hello sir how can we replace r with p can you please give a generalised methodo for such substitution
_________________

First of all a proper GMAT question would mention that Q doesn't equal to zero (as it's in denominator).

Next, we don't need R at all, substitute it. The question becomes is \(\frac{P}{Q}\leq{P}\)? Notice that we can not reduce both sides by P since we don't know the sign of it, thus don't know whether we should flip the sign of the inequality when reducing.

(1) P>50 --> P is positive - reduce by it. The question becomes is \(\frac{1}{Q}\leq{1}\)? --> is \(Q<0\) or \(Q\geq{1}\)? We don't know that. Not sufficient.

(2) 0<Q≤20. No info about P. Not sufficient.

(1)+(2) From (1) the question became: is \(Q<0\) or \(Q\geq{1}\)? Now, (2) says \(0<Q\leq{20}\), which is not sufficient to answer the question definitely: if \(1\leq{Q}\leq{20}\) the answer is YES but if \(0<Q<1\) the answer is NO. Not sufficient.

Answer: E.

Hope it's clear.

hello sir how can we replace r with p can you please give a generalised methodo for such substitution

We are given that R=P/Q, so we can substitute R with P/Q (not with P).
_________________

Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink]

Show Tags

07 Feb 2014, 11:31

wizard wrote:

If R=P/Q, is R≤P?

(1) P>50 (2) 0<Q≤20

r=p/q---> or qr=p..

question is r<=p?

How i solved this question ...

st(1)---> p>50.. insufficient as we dont know value of p r and q.

St(2).... its also insufficient.. because we dont knw the value of other variables..

Togather st(1) and (2)..

qr=p .. Suppose ..q=1 and p=50.. then p will be 50.. ans wil be YES.. because p=r... If lets suppose Q=1/2.. and p=50.. then r will be 100 ans will be no r>p..

so Ans is E..
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

We don't need R at all, so substitute it. The question becomes is \(\frac{P}{Q}\leq{P}\)? Notice that we can not reduce both sides by P since we don't know the sign of it, thus don't know whether we should flip the sign of the inequality when reducing.

(1) P>50 --> P is positive - reduce by it. The question becomes is \(\frac{1}{Q}\leq{1}\)? --> is \(Q<0\) or \(Q\geq{1}\)? We don't know that. Not sufficient.

(2) 0<Q≤20. No info about P. Not sufficient.

(1)+(2) From (1) the question became: is \(Q<0\) or \(Q\geq{1}\)? Now, (2) says \(0<Q\leq{20}\), which is not sufficient to answer the question definitely: if \(1\leq{Q}\leq{20}\) the answer is YES but if \(0<Q<1\) the answer is NO. Not sufficient.

Answer: E.

Hope it's clear.

How we got \(Q<0\)? I understand that for \(\frac{1}{Q} \leq1\) Q could be either \(Q\leq{1}\) or \(Q <0\) but then again I can say \(Q=0\)

We don't need R at all, so substitute it. The question becomes is \(\frac{P}{Q}\leq{P}\)? Notice that we can not reduce both sides by P since we don't know the sign of it, thus don't know whether we should flip the sign of the inequality when reducing.

(1) P>50 --> P is positive - reduce by it. The question becomes is \(\frac{1}{Q}\leq{1}\)? --> is \(Q<0\) or \(Q\geq{1}\)? We don't know that. Not sufficient.

(2) 0<Q≤20. No info about P. Not sufficient.

(1)+(2) From (1) the question became: is \(Q<0\) or \(Q\geq{1}\)? Now, (2) says \(0<Q\leq{20}\), which is not sufficient to answer the question definitely: if \(1\leq{Q}\leq{20}\) the answer is YES but if \(0<Q<1\) the answer is NO. Not sufficient.

Answer: E.

Hope it's clear.

How we got \(Q<0\)? I understand that for \(\frac{1}{Q} \leq1\) Q could be either \(Q\leq{1}\) or \(Q <0\) but then again I can say \(Q=0\)

If Q=0, then \(\frac{1}{Q}\) is undefined, not \(\leq1\), so Q cannot be 0.

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