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If R = P/Q, is R P? (1) P > 50 (2) 0 < Q 20   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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If R = P/Q, is R P? (1) P > 50 (2) 0 < Q 20   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.

Answer: E.

Hope it's clear.
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If R = P/Q, is R P? (1) P > 50 (2) 0 < Q 20   29 Aug 2012, 00:25
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doesn't combining (1)+(2) imply 1<=q<=2, common region implied by options
(1) and (2)
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If R = P/Q, is R P? (1) P > 50 (2) 0 < Q 20   29 Aug 2012, 01:24
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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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If R = P/Q, is R P? (1) P > 50 (2) 0 < Q 20   29 Aug 2012, 11:00
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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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If R = P/Q, is R P? (1) P > 50 (2) 0 < Q 20   30 Aug 2012, 01:56
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Ankit04041987
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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If R = P/Q, is R P? (1) P > 50 (2) 0 < Q 20   30 Aug 2012, 20:02
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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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If R = P/Q, is R P? (1) P > 50 (2) 0 < Q 20   31 Aug 2012, 00:10
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Bunuel
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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If R = P/Q, is R P? (1) P > 50 (2) 0 < Q 20   03 Jun 2014, 08:08
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Bunuel
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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If R = P/Q, is R P? (1) P > 50 (2) 0 < Q 20   03 Jun 2014, 08:35
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Bunuel
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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If R = P/Q, is R P? (1) P > 50 (2) 0 < Q 20   07 Nov 2023, 11:12
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