Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 07 Feb 2016, 14:46

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Intern
Joined: 17 Oct 2011
Posts: 27
Location: Taiwan
GMAT 1: 590 Q39 V34
GMAT 2: 680 Q47 V35
Followers: 0

Kudos [?]: 32 [0], given: 10

If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink]  22 Feb 2012, 02:01
5
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

50% (01:57) correct 50% (01:20) wrong based on 131 sessions
If R=P/Q, is R≤P?

(1) P>50
(2) 0<Q≤20
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5345

Kudos [?]: 62113 [5] , given: 9440

Re: If R=P/Q, is R≤P? [#permalink]  22 Feb 2012, 02:18
5
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.

Hope it's clear.
_________________
Manager
Joined: 01 Aug 2011
Posts: 84
Location: India
Concentration: Finance, Finance
GPA: 3.4
Followers: 2

Kudos [?]: 103 [0], given: 29

Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink]  28 Aug 2012, 23:25
doesn't combining (1)+(2) imply 1<=q<=2, common region implied by options
(1) and (2)
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5345

Kudos [?]: 62113 [0], given: 9440

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.

Hope it's clear.
_________________
Manager
Joined: 01 Aug 2011
Posts: 84
Location: India
Concentration: Finance, Finance
GPA: 3.4
Followers: 2

Kudos [?]: 103 [0], given: 29

Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink]  29 Aug 2012, 10:00

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
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5345

Kudos [?]: 62113 [0], given: 9440

Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink]  30 Aug 2012, 00:56
Expert's post
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 $$Q\geq{1}$$?
_________________
Manager
Joined: 01 Aug 2011
Posts: 84
Location: India
Concentration: Finance, Finance
GPA: 3.4
Followers: 2

Kudos [?]: 103 [0], given: 29

Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink]  30 Aug 2012, 09:24
got it , thnx a lot Bunuel
Manager
Status: exam is close ... dont know if i ll hit that number
Joined: 06 Jun 2011
Posts: 206
Location: India
GMAT Date: 10-09-2012
GPA: 3.2
Followers: 2

Kudos [?]: 18 [0], given: 1

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.

Hope it's clear.

hello sir
how can we replace r with p
can you please give a generalised methodo for such substitution
_________________

just one more month for exam...

Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5345

Kudos [?]: 62113 [0], given: 9440

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.

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).
_________________
Intern
Joined: 17 Sep 2011
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 3

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

Posted from my mobile device
Intern
Joined: 28 Aug 2012
Posts: 46
Location: Austria
GMAT 1: 770 Q51 V42
Followers: 3

Kudos [?]: 38 [0], given: 3

Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink]  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.
Senior Manager
Joined: 06 Aug 2011
Posts: 405
Followers: 2

Kudos [?]: 137 [0], given: 82

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 !

Current Student
Joined: 21 Oct 2013
Posts: 194
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Followers: 1

Kudos [?]: 26 [0], given: 19

Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink]  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.
Senior Manager
Joined: 25 Sep 2012
Posts: 288
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Followers: 0

Kudos [?]: 100 [0], given: 237

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.

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 $$Q=0$$
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5345

Kudos [?]: 62113 [1] , given: 9440

Re: If R=P/Q, is R≤P? [#permalink]  03 Jun 2014, 07:35
1
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.

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?
_________________
Senior Manager
Joined: 27 Oct 2013
Posts: 260
Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
Followers: 1

Kudos [?]: 99 [0], given: 79

Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink]  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
VP
Joined: 17 Jul 2014
Posts: 1040
Location: United States
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GPA: 3.56
Followers: 8

Kudos [?]: 111 [0], given: 80

Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20 [#permalink]  22 Oct 2015, 06:15
Q can be >1 or can be between 0 and 1. Since neither statement removes this ambiguity, the answer is E.
Re: If R=P/Q, is R≤P? (1) P>50 (2) 0<Q≤20   [#permalink] 22 Oct 2015, 06:15
Similar topics Replies Last post
Similar
Topics:
If w and c are integers, is w > 0? (1) w + c > 50 (2) c > 48 2 03 Sep 2011, 02:19
3 If w and c are integers is w > 0 ? (1) w + c > 50 (2) 7 16 Dec 2010, 04:28
What is the value of p^3 + 2p ? (1) p^2 5p + 4 = 0. (2) The 3 11 Jun 2010, 08:35
Is 1/p > r/(r^2+2) ? 1. p = r 2. r > 0 Can 6 20 Mar 2010, 22:17
1 Is 3^p > 2^q ? (1) q = 2p (2) q > 0 4 28 Jun 2007, 07:18
Display posts from previous: Sort by