Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: If R=P/Q, is R≤P? [#permalink]
22 Feb 2012, 02:18

4

This post received KUDOS

Expert's post

If R=P/Q, is R≤P?

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.

Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink]
29 Aug 2012, 00:24

Expert's post

Ankit04041987 wrote:

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.

Re: If R=P/Q, is R≤P? [#permalink]
30 Aug 2012, 19:02

Bunuel wrote:

If R=P/Q, is R≤P?

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 _________________

Re: If R=P/Q, is R≤P? [#permalink]
30 Aug 2012, 23:10

Expert's post

mohan514 wrote:

Bunuel wrote:

If R=P/Q, is R≤P?

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]
07 Feb 2014, 10:31

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 !

Re: If R=P/Q, is R≤P? [#permalink]
03 Jun 2014, 07:08

Bunuel wrote:

If R=P/Q, is R≤P?

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

Re: If R=P/Q, is R≤P? [#permalink]
03 Jun 2014, 07:35

1

This post received KUDOS

Expert's post

b2bt wrote:

Bunuel wrote:

If R=P/Q, is R≤P?

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.

I couldn’t help myself but stay impressed. young leader who can now basically speak Chinese and handle things alone (I’m Korean Canadian by the way, so...