It is currently 14 Dec 2017, 16:51

### 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

# Events & Promotions

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

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 10 Jul 2016
Posts: 10

Kudos [?]: 36 [0], given: 40

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

### Show Tags

23 Jan 2017, 02:40
7
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

48% (02:11) correct 52% (01:57) wrong based on 147 sessions

### HideShow 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
[Reveal] Spoiler: OA

Kudos [?]: 36 [0], given: 40

Math Expert
Joined: 02 Aug 2009
Posts: 5349

Kudos [?]: 6128 [3], given: 121

Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink]

### Show Tags

23 Jan 2017, 03:32
3
This post received
KUDOS
Expert's post
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=35p/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... Wrong

Only B is correct
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6128 [3], given: 121

Board of Directors
Joined: 17 Jul 2014
Posts: 2698

Kudos [?]: 450 [0], given: 208

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink]

### Show Tags

23 Jan 2017, 15:27
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.

Kudos [?]: 450 [0], given: 208

Intern
Joined: 15 Jun 2013
Posts: 47

Kudos [?]: 14 [0], given: 33

Schools: Ivey '19 (I)
GMAT 1: 690 Q49 V35
GPA: 3.82
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink]

### Show Tags

31 May 2017, 09:30
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.

Kudos [?]: 14 [0], given: 33

Intern
Joined: 17 Dec 2016
Posts: 2

Kudos [?]: 7 [5], given: 6

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

### Show Tags

08 Jun 2017, 10:15
5
This post received
KUDOS
1
This post was
BOOKMARKED
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

Kudos [?]: 7 [5], given: 6

Manager
Joined: 23 May 2017
Posts: 161

Kudos [?]: 56 [1], given: 7

Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink]

### Show Tags

08 Jun 2017, 10:25
1
This post received
KUDOS
Attachment:

FullSizeRender (4).jpg [ 64.61 KiB | Viewed 1162 times ]

ANS: B
_________________

If you like the post, please award me Kudos!! It motivates me

Kudos [?]: 56 [1], given: 7

Intern
Joined: 06 Sep 2013
Posts: 34

Kudos [?]: 20 [0], given: 284

Location: India
Concentration: Leadership, Strategy
Schools: ISB '19 (A)
GMAT 1: 770 Q50 V44
GPA: 3.7
WE: Information Technology (Consulting)
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink]

### Show Tags

08 Jun 2017, 10:56
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??

Kudos [?]: 20 [0], given: 284

Manager
Joined: 18 Jun 2017
Posts: 60

Kudos [?]: 2 [0], given: 166

Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink]

### Show Tags

10 Jul 2017, 07:02
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.

Kudos [?]: 2 [0], given: 166

Intern
Joined: 08 Aug 2017
Posts: 3

Kudos [?]: 5 [0], given: 150

WE: Analyst (Investment Banking)
Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and [#permalink]

### Show Tags

13 Oct 2017, 06:20
$$50P + 100Q = R(P + Q)$$

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

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

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

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

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.

Kudos [?]: 5 [0], given: 150

Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and   [#permalink] 13 Oct 2017, 06:20
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.