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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.

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