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If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20
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22 Feb 2012, 03:01
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If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20
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Re: If R=P/Q, is R≤P?
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22 Feb 2012, 03:18
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
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29 Aug 2012, 00:25
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
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29 Aug 2012, 01:24
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
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29 Aug 2012, 11:00
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
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30 Aug 2012, 01:56
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
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30 Aug 2012, 10:24
got it , thnx a lot Bunuel



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Re: If R=P/Q, is R≤P?
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30 Aug 2012, 20:02
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?
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31 Aug 2012, 00:10
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 pcan 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
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02 Sep 2012, 00:57
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
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02 Sep 2012, 01:25
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
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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..
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Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20
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13 Feb 2014, 03:43
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?
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03 Jun 2014, 08:08
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?
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03 Jun 2014, 08:35
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
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03 Jun 2014, 22:35
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



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If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20
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22 Oct 2015, 07:15
Q can be >1 or can be between 0 and 1. Since neither statement removes this ambiguity, the answer is E. or: I took the question to be: is Q=1 or 0<Q<1? 1. doesn't tell much. AD  out 2. 0<Q<=20  doesn't tell much about P. Plus Q can be >1 or can be between 0 and 1. B out. 1+2 P=60, Q=3 > R=20. answer to our question is yes. P=60, Q=1/2 => R=120. answer is no. E.
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Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20
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