NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 20:38 It is currently 24 Apr 2024, 20:38
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
S
siddharthsinha123
Intern
Intern
Joined: 10 Jul 2016
Posts: 32
Own Kudos [?]: 183 [35]
Given Kudos: 85
Send PM
GMAT ToolKit User Reviews Badge
If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   23 Jan 2017, 03:40
4
Kudos
31
Bookmarks
00:00
A
B
C
D
E

Difficulty:

85% (hard)

Question Stats:

51% (02:27) correct 49% (02:30) wrong based on 331 sessions
Hide Show timer Statistics
If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and if P>Q, which of the following could be the value of R?

A. 50
B. 65
C. 75
D. 90
E. 100
ShowHide Answer
Official Answer
B
Most Helpful Reply
avatar
B
rohitchauhan10
Intern
Intern
Joined: 17 Dec 2016
Posts: 3
Own Kudos [?]: 17 [16]
Given Kudos: 41
Send PM
If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   08 Jun 2017, 11:15
15
Kudos
1
Bookmarks
Hi

Simplest method would be to re-arrange the given statement as :

(50P + 100Q)/(P+Q) = R

From this you know that this is nothing but weighted average. It is given that P > Q, hence the average would be closer to 50 than to 100 and not in the middle value (75). You are left with only 65 (B).

Thanks
Rohit
User avatar
S
Leo8
Manager
Manager
Joined: 23 May 2017
Posts: 192
Own Kudos [?]: 359 [11]
Given Kudos: 9
Concentration: Finance, Accounting
WE:Programming (Energy and Utilities)
Send PM
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   08 Jun 2017, 11:25
10
Kudos
1
Bookmarks
Attachment:
FullSizeRender (4).jpg
FullSizeRender (4).jpg [ 64.61 KiB | Viewed 17003 times ]


ANS: B
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11170
Own Kudos [?]: 31894 [8]
Given Kudos: 290
Send PM
Reviews Badge
If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   23 Jan 2017, 04:32
8
Kudos
Expert Reply
siddharthsinha123 wrote:
If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and if P>Q, which of the following could be the value of R?

A. 50
B. 65
C. 75
D. 90
E. 100



Hi,
Easiest way would be to substitute choices in given equation 50p+100q=r(p+q) and check for P>Q..

A. 50.....\(50p+100q=50(p+q)....50p+100q=50p+50q....100q=50q\)... Wrong
B. 65.....\(50p+100q=65(p+q)....50p+100q=65p+65q....35q=15p... p=\frac{35q}{15}...P>Q\).. Correct
C. 75.....\(50p+100q=75(p+q)....50p+100q=75p+75q....25q=25p.. P=Q\).... Wrong
D. 90.....\(50p+100q=90(p+q)....50p+100q=90p+90q....10q=40p.. ..P<Q\)..Wrong
E. 100.....\(50p+100q=100(p+q)....50p+100q=100p+100q....100p=50p....P=0\)... Wrong

Only B is correct
General Discussion
avatar
B
nitesh181989
Intern
Intern
Joined: 06 Sep 2013
Posts: 29
Own Kudos [?]: 34 [2]
Given Kudos: 284
Location: India
Concentration: Leadership, Strategy
Schools: ISB '19 (A)
GMAT 1: 770 Q50 V44
GPA: 3.7
WE:Information Technology (Consulting)
Send PM
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   08 Jun 2017, 11:56
2
Kudos
Leo8 wrote:
Attachment:
FullSizeRender (4).jpg


ANS: B


One doubt...

P(50-R) = Q(R-100)
P/Q=(R-100)/(50-R)------(1)
Also, P>Q
IMPLIES P/Q>1
BUT FROM eq (1), this means
(R-100)/(50-R) > 1
R-100>50-R
2R>150
R>75

Which is opposite of what you have shown.

Can you spot the issue with my approach??
User avatar
P
hellosanthosh2k2
Senior Manager
Senior Manager
Joined: 02 Apr 2014
Posts: 371
Own Kudos [?]: 474 [2]
Given Kudos: 1227
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5
Send PM
If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   06 Jan 2018, 06:34
2
Kudos
Can be easily solved using weight average concept.

Given: 50 ----------------R------------------100
weight:P--------------------------------------Q
if P = Q, then R will be at centre i.e = 75
however given, P > Q, weighted average will be pulled towards 50 and will be less than 75
only choice B fits perfectly, as weighted average can't be equal to 50 (since P = 50)

Kudos please, if you like my approach, need to unlock my gmat club tests

Thanks
User avatar
P
mvictor
Board of Directors
Joined: 17 Jul 2014
Posts: 2163
Own Kudos [?]: 1180 [1]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Send PM
GMAT ToolKit User Reviews Badge
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   23 Jan 2017, 16:27
1
Bookmarks
siddharthsinha123 wrote:
If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and if P>Q, which of the following could be the value of R?

A. 50
B. 65
C. 75
D. 90
E. 100



I got to B easily through few steps...
100Q-RQ = RP - 50P
Q(100-R) = P(R-50)
from the above, we can get:
50<R<100
A and E are right away out.

if R =90, then 100-R=10 and 100-50 = 50, but this doesn't satisfy the condition P>Q, but rather vice versa Q>P - D is out.

at least we got now a 50% chance to get the right answer, m? :D

let's try C:
100-75=25
75-50=25

25Q=25P -> P=Q -> doesn't satisfy the condition P>Q

the only option left is B.
avatar
B
malevg
Intern
Intern
Joined: 15 Jun 2013
Posts: 33
Own Kudos [?]: 17 [0]
Given Kudos: 33
Schools: Ivey '19 (I)
GMAT 1: 690 Q49 V35
GPA: 3.82
Send PM
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   31 May 2017, 10:30
siddharthsinha123 wrote:
If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and if P>Q, which of the following could be the value of R?

A. 50
B. 65
C. 75
D. 90
E. 100


From the equation above we see that P(50-R)+Q(100-R)=0.
Therefore R<>50 or 100, so A and E are out. Also, P<>Q so C is out. Now we see that P will be with negative sign and Q - with Positive. Taking into account that P>Q |50-R| should be <|100-R|. Thus B is the answer |50-65|=15<|100-65|=35 (with D it would be |50-90|=40>|100-90|=10.
avatar
B
FB2017
Manager
Manager
Joined: 18 Jun 2017
Posts: 50
Own Kudos [?]: 13 [1]
Given Kudos: 165
Send PM
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   10 Jul 2017, 08:02
On substituting the equation R=65 then the we have 35q=15p... or p=35q/15...P>Q..
But this value can be non integer if q=1,2.... etc then doesn't it violate the statement that P,Q and R are positive integers.

Please advise.
avatar
B
varodriguezh
Intern
Intern
Joined: 08 Aug 2017
Posts: 2
Own Kudos [?]: 6 [0]
Given Kudos: 153
WE:Analyst (Investment Banking)
Send PM
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   13 Oct 2017, 07:20
\(50P + 100Q = R(P + Q)\)

\(50(P + 2Q) = R(P + Q)\)

\(50[(P + Q) + Q] = R(P + Q)\)

\(50Q = (R - 50)(P + Q)\)

\(\frac{Q}{(P + Q)}= \frac{(R - 50)}{50}\)

Let's try with the answer in the middle (C) \(R=75 => \frac{(75 - 50)}{50}= \frac{25}{50} = \frac{1}{2} => \frac{Q}{(P + Q)}= \frac{1}{2}\) => Q=1 and P=1, which cannot be (P must be greater than Q). With this, the bigger answers D and E (90 and 100) cannot be either.

Let's with B: \(R=65 => \frac{(65 - 50)}{50}= \frac{15}{50} = \frac{3}{10} => \frac{Q}{(P + Q)}= \frac{3}{10}\) => Q=3 and P=7, and this matches with the statement which says that P > Q. => Correct Answer: B.
avatar
B
rahulkashyap
Manager
Manager
Joined: 09 Oct 2015
Posts: 174
Own Kudos [?]: 61 [0]
Given Kudos: 28
Send PM
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   06 Jan 2018, 07:15
Leo8 wrote:
Attachment:
FullSizeRender (4).jpg


ANS: B


can u explain how you got 50-r as greater
User avatar
S
Leo8
Manager
Manager
Joined: 23 May 2017
Posts: 192
Own Kudos [?]: 359 [0]
Given Kudos: 9
Concentration: Finance, Accounting
WE:Programming (Energy and Utilities)
Send PM
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   06 Jan 2018, 10:13
rahulkashyap wrote:
Leo8 wrote:
Attachment:
FullSizeRender (4).jpg


ANS: B


can u explain how you got 50-r as greater




from our equation :

P(50 -R) = Q( R - 100)

But Its given P > Q so for the equality to be true the co-effficent of P must be greater than co-efficient of Q

50 - R > R - 100

also nitesh181989 :

P/q > 1 will give you equation : 50 - R > R - 100

you have put co-effiecient of Q in the numerator and that of P in denominator
avatar
B
rahulkashyap
Manager
Manager
Joined: 09 Oct 2015
Posts: 174
Own Kudos [?]: 61 [0]
Given Kudos: 28
Send PM
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   06 Jan 2018, 10:37
Leo8 wrote:
rahulkashyap wrote:
Leo8 wrote:
Attachment:
FullSizeRender (4).jpg


ANS: B


can u explain how you got 50-r as greater




from our equation :

P(50 -R) = Q( R - 100)

But Its given P > Q so for the equality to be true the co-effficent of P must be greater than co-efficient of Q

50 - R > R - 100

also nitesh181989 :

P/q > 1 will give you equation : 50 - R > R - 100

you have put co-effiecient of Q in the numerator and that of P in denominator


Well, first of all if p if greater than q, the inequality sign should be there other way. Not what you've pointed. (bigger) x (smaller)= (smaller) x(bigger)
Even then, you don't know whether lhs and rhs are both positive / negative. So you can't say with certainty

Posted from my mobile device
User avatar
B
avirupm97
Intern
Intern
Joined: 26 Jan 2023
Posts: 27
Own Kudos [?]: 20 [0]
Given Kudos: 89
Location: India
Concentration: Technology, Entrepreneurship
WE:General Management (Computer Software)
Send PM
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   10 Jun 2023, 07:26
chetan2u wrote:
siddharthsinha123 wrote:
If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and if P>Q, which of the following could be the value of R?

A. 50
B. 65
C. 75
D. 90
E. 100



Hi,
Easiest way would be to substitute choices in given equation 50p+100q=r(p+q) and check for P>Q..

A. 50.....\(50p+100q=50(p+q)....50p+100q=50p+50q....100q=50q\)... Wrong
B. 65.....\(50p+100q=65(p+q)....50p+100q=65p+65q....35q=15p... p=\frac{35q}{15}...P>Q\).. Correct
C. 75.....\(50p+100q=75(p+q)....50p+100q=75p+75q....25q=25p.. P=Q\).... Wrong
D. 90.....\(50p+100q=90(p+q)....50p+100q=90p+90q....10q=40p.. ..P<Q\)..Wrong
E. 100.....\(50p+100q=100(p+q)....50p+100q=100p+100q....100p=50p....P=0\)... Wrong

Only B is correct


Hi chetan2u, Might be silly but would this approach work as well?

=50p+100q=r(p+q)
=50p + 100q/(p+q) = r
=50p + 50q + 50q/(p+q) = r
=50 + 50q/(p+q) = r ......(The answer will be > 50 but always less than 75 because 50q/(p+q) can never be >=25 since p>q )
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11170
Own Kudos [?]: 31894 [0]
Given Kudos: 290
Send PM
Reviews Badge
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   10 Jun 2023, 08:56
Expert Reply
avirupm97 wrote:
chetan2u wrote:
siddharthsinha123 wrote:
If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and if P>Q, which of the following could be the value of R?

A. 50
B. 65
C. 75
D. 90
E. 100



Hi,
Easiest way would be to substitute choices in given equation 50p+100q=r(p+q) and check for P>Q..

A. 50.....\(50p+100q=50(p+q)....50p+100q=50p+50q....100q=50q\)... Wrong
B. 65.....\(50p+100q=65(p+q)....50p+100q=65p+65q....35q=15p... p=\frac{35q}{15}...P>Q\).. Correct
C. 75.....\(50p+100q=75(p+q)....50p+100q=75p+75q....25q=25p.. P=Q\).... Wrong
D. 90.....\(50p+100q=90(p+q)....50p+100q=90p+90q....10q=40p.. ..P<Q\)..Wrong
E. 100.....\(50p+100q=100(p+q)....50p+100q=100p+100q....100p=50p....P=0\)... Wrong

Only B is correct


Hi chetan2u, Might be silly but would this approach work as well?

=50p+100q=r(p+q)
=50p + 100q/(p+q) = r
=50p + 50q + 50q/(p+q) = r
=50 + 50q/(p+q) = r ......(The answer will be > 50 but always less than 75 because 50q/(p+q) can never be >=25 since p>q )


That’s a perfectly fine solution. No error at all.
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5343
Own Kudos [?]: 3964 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink] New post   10 Jun 2023, 09:06
Asked: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and if P>Q, which of the following could be the value of R?

50P + 100Q = R (P + Q)
(50-R)P + (100-R)Q = 0
P = (100-R)Q/(R-50)
Since P > Q
(100-R)Q/(R-50) > Q
(100-R) > R-50
R < 75

Since P > 0
(100-R)Q/(R-50) > 0
R < 100
R > 50

IMO B
GMAT Club Bot
gmatclubot
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink]
10 Jun 2023, 09:06
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions