Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 10 Jul 2016
Posts: 44

If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and
[#permalink]
Show Tags
23 Jan 2017, 03:40
Question Stats:
52% (02:39) correct 48% (02:33) wrong based on 157 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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Aug 2009
Posts: 7984

If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and
[#permalink]
Show Tags
23 Jan 2017, 04:32
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
_________________




Intern
Joined: 17 Dec 2016
Posts: 2

If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and
[#permalink]
Show Tags
08 Jun 2017, 11:15
Hi
Simplest method would be to rearrange 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




Board of Directors
Joined: 17 Jul 2014
Posts: 2509
Location: United States (IL)
Concentration: Finance, Economics
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, 16:27
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... 100QRQ = RP  50P Q(100R) = P(R50) from the above, we can get: 50<R<100 A and E are right away out. if R =90, then 100R=10 and 10050 = 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: 10075=25 7550=25 25Q=25P > P=Q > doesn't satisfy the condition P>Q the only option left is B.



Intern
Joined: 15 Jun 2013
Posts: 46
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, 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(50R)+Q(100R)=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 50R should be <100R. Thus B is the answer 5065=15<10065=35 (with D it would be 5090=40>10090=10.



Manager
Joined: 23 May 2017
Posts: 234
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, 11:25
Attachment:
FullSizeRender (4).jpg [ 64.61 KiB  Viewed 4596 times ]
ANS: B
_________________
If you like the post, please award me Kudos!! It motivates me



Current Student
Joined: 06 Sep 2013
Posts: 33
Location: India
Concentration: Leadership, Strategy
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, 11:56
Leo8 wrote: Attachment: FullSizeRender (4).jpg ANS: B One doubt... P(50R) = Q(R100) P/Q=(R100)/(50R)(1) Also, P>Q IMPLIES P/Q>1 BUT FROM eq (1), this means (R100)/(50R) > 1 R100>50R 2R>150 R>75 Which is opposite of what you have shown. Can you spot the issue with my approach??



Manager
Joined: 18 Jun 2017
Posts: 58

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



Intern
Joined: 08 Aug 2017
Posts: 3
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, 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.



Senior Manager
Joined: 02 Apr 2014
Posts: 468
Location: India
GPA: 3.5

If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and
[#permalink]
Show Tags
06 Jan 2018, 06:34
Can be easily solved using weight average concept. Given: 50 R100 weight:PQ 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 testsThanks



Manager
Joined: 09 Oct 2015
Posts: 225

Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and
[#permalink]
Show Tags
06 Jan 2018, 07:15
Leo8 wrote: Attachment: FullSizeRender (4).jpg ANS: B can u explain how you got 50r as greater



Manager
Joined: 23 May 2017
Posts: 234
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
06 Jan 2018, 10:13
rahulkashyap wrote: Leo8 wrote: Attachment: FullSizeRender (4).jpg ANS: B can u explain how you got 50r as greater from our equation : P(50 R) = Q( R  100) But Its given P > Q so for the equality to be true the coeffficent of P must be greater than coefficient of Q 50  R > R  100 also nitesh181989 : P/q > 1 will give you equation : 50  R > R  100 you have put coeffiecient of Q in the numerator and that of P in denominator
_________________
If you like the post, please award me Kudos!! It motivates me



Manager
Joined: 09 Oct 2015
Posts: 225

Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and
[#permalink]
Show Tags
06 Jan 2018, 10:37
Leo8 wrote: rahulkashyap wrote: Leo8 wrote: Attachment: FullSizeRender (4).jpg ANS: B can u explain how you got 50r as greater from our equation : P(50 R) = Q( R  100) But Its given P > Q so for the equality to be true the coeffficent of P must be greater than coefficient of Q 50  R > R  100 also nitesh181989 : P/q > 1 will give you equation : 50  R > R  100 you have put coeffiecient 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



NonHuman User
Joined: 09 Sep 2013
Posts: 13277

Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and
[#permalink]
Show Tags
16 Apr 2019, 09:44
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: If P,Q and R are positive integers such that 50P + 100Q = R(P + Q) and
[#permalink]
16 Apr 2019, 09:44






