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If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20

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If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink] New post 22 Feb 2012, 02:01
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If R=P/Q, is R≤P?

(1) P>50
(2) 0<Q≤20
[Reveal] Spoiler: OA
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Re: If R=P/Q, is R≤P? [#permalink] New post 22 Feb 2012, 02:18
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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.
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Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink] New post 28 Aug 2012, 23:25
doesn't combining (1)+(2) imply 1<=q<=2, common region implied by options
(1) and (2)
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Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink] New post 29 Aug 2012, 00:24
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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.

Hope it's clear.
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Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink] New post 29 Aug 2012, 10:00
Thanks for your reply

I think you dint get my problem

what i want to ask is

option1 states Q<0 or Q>=1

option2 states 1<=Q<=20,cant 1 and 2 be combined to say that Q definitely lies between 1 and 20

and in that case 1/q will definitely be <=1

and c will be the answer
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Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink] New post 30 Aug 2012, 00:56
Expert's post
Ankit04041987 wrote:
Thanks for your reply

I think you dint get my problem

what i want to ask is

option1 states Q<0 or Q>=1

option2 states 1<=Q<=20,cant 1 and 2 be combined to say that Q definitely lies between 1 and 20

and in that case 1/q will definitely be <=1

and c will be the answer


The red part is not correct.

We are not given in (1) that Q<0 or Q\geq{1}.

From (1) the question became: is \frac{1}{Q}\leq{1}? Or which is the same: is Q<0 or Q\geq{1}?
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Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink] New post 30 Aug 2012, 09:24
got it , thnx a lot Bunuel :-)
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Re: If R=P/Q, is R≤P? [#permalink] New post 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
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Re: If R=P/Q, is R≤P? [#permalink] New post 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).
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Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink] New post 01 Sep 2012, 23:57
P>50 --> P is positive - reduce by it. The question becomes is ? --> is or ? We don't know that. Not sufficient.

Hi bunuel,
Can u pl explain on how did you deduce that is Q<0 from stmt 1?

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Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink] New post 02 Sep 2012, 00:25
urshohini wrote:
Can u pl explain on how did you deduce that is Q<0 from stmt 1?
Because if q is negative, 1/q will be negative, which is smaller than +1.
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Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink] New post 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..
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Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink] New post 13 Feb 2014, 02:43
I solved like this: R would be always <= P except Q is 1. So we need to know Q.

(1) P > 50 --> No info about Q, so IS.
(2) 0<Q<=20 --> No definite value for Q. IS.

Together still not enough information about Q.

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

Does this make sense?
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Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink] New post 03 Jun 2014, 21:35
Statement 1 and Statement 2 alone are not sufficient...

Combining the two statements...
p q Statement1 Satisfied?||| Statement2 Satisfied?||| Answer to the question?
52 13 Yes Yes Yes
52 1/2 Yes Yes No

Hence E
Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20   [#permalink] 03 Jun 2014, 21:35
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