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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]

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22 Feb 2012, 03:01
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51% (02:01) correct 49% (01:23) wrong based on 148 sessions

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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]

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22 Feb 2012, 03:18
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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.

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

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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 [#permalink]

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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 [#permalink]

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29 Aug 2012, 11:00

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]

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30 Aug 2012, 01:56
Ankit04041987 wrote:

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]

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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? [#permalink]

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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.

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]

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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.

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]

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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 [#permalink]

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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 [#permalink]

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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 [#permalink]

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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? [#permalink]

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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.

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]

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03 Jun 2014, 08:35
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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.

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]

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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 [#permalink]

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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.
If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20   [#permalink] 22 Oct 2015, 07:15
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