Last visit was: 15 Dec 2024, 01:46 It is currently 15 Dec 2024, 01:46
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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
Back to Forum
Create Topic
User avatar
susheelh
User avatar
Joined: 12 Jun 2016
Last visit: 13 Jun 2018
Posts: 144
Own Kudos:
249
 []
Given Kudos: 151
Location: India
Concentration: Technology, Leadership
WE:Sales (Telecommunications)
Posts: 144
Kudos: 249
 []
If P, Q and R are Positive numbers - Which "Can" be the value of R? 27 Jul 2016, 03:36
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

45% (02:26) correct 55% (02:37) wrong based on 104 sessions

History

Date
Time
Result
Not Attempted Yet
P, Q and R are positive numbers satisfying \(\frac{P}{(P+Q)}*(30) + \frac{Q}{(P+Q)}*(90) = R\). P<Q. Which of the following can be a value of R?

A. 30
B. 45
C. 60
D. 75
E. 90
ShowHide Answer
Official Answer
D
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Dec 2024
Posts: 97,878
Own Kudos:
685,951
Given Kudos: 88,272
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,878
Kudos: 685,951
If P, Q and R are Positive numbers - Which "Can" be the value of R? 27 Jul 2016, 03:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
susheelh
P, Q and R are positive numbers satisfying \(\frac{P}{(P+Q)}*(30) + \frac{Q}{(P+Q)}*(90) = R\). P<Q. Which of the following can be a value of R?

A. 30
B. 45
C. 60
D. 75
E. 90

This is a copy of the following question: if-x-y-and-k-are-positive-numbers-such-that-x-x-y-128231.html
User avatar
abhimahna
User avatar
Board of Directors
Joined: 18 Jul 2015
Last visit: 06 Jul 2024
Posts: 3,570
Own Kudos:
5,591
Given Kudos: 346
Status:Emory Goizueta Alum
Products:
My Reviews
Expert reply
Posts: 3,570
Kudos: 5,591
If P, Q and R are Positive numbers - Which "Can" be the value of R? 27 Jul 2016, 04:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
susheelh
P, Q and R are positive numbers satisfying \(\frac{P}{(P+Q)}*(30) + \frac{Q}{(P+Q)}*(90) = R\). P<Q. Which of the following can be a value of R?

A. 30
B. 45
C. 60
D. 75
E. 90

Put the value of R from he options into the above equation.

for r=30, 30p/(p+q) + 90q/(p+q) =30=> P=Q. But we have p<q in the question. hence incorrect.

For r=45, P=3q

For r=60, P=Q

For r=75, Q=3p. Valid condition. Hence the answer.
User avatar
AtifS
User avatar
Joined: 20 Jan 2010
Last visit: 04 Jan 2017
Posts: 217
Own Kudos:
464
Given Kudos: 260
Status:Not afraid of failures, disappointments, and falls.
Concentration: Technology, Entrepreneurship
Schools: Haas '19 Darden '19 INSEAD Jan '19 Stanford '19 Anderson '19 HBS '19
WE:Operations (Telecommunications)
Schools: Haas '19 Darden '19 INSEAD Jan '19 Stanford '19 Anderson '19 HBS '19
Posts: 217
Kudos: 464
If P, Q and R are Positive numbers - Which "Can" be the value of R? 27 Jul 2016, 05:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Actualy, I got it wrong but realised soon that why am I wrong.

R = {p/(p+q)}*30 + {q/(p+q)}*90 --> 30 * [{p/(p+q)} + {3q/(p+q)}] --> 30 * { (p+3q)/(p+q)} --> 30* { (p+q+2q)/(p+q) } --> 30 * { (p+q)/(p+q) + 2q/(p+q) } --> 30* {1 + 2q/(p+q)} --> 30 + {60q/(p+q)} --> now by plugging in +ve numbers and we know that p<q so, let's take p =1 & q = 2 --> 30 + {60 *2/(1+2)} --> 30 + 120/3 --> 30 + 40 --> R = 70, but it isn't in the choices and also from this we can see that answers can't be less than 70, so eliminate options A, B, and C.
Let's quickly try other numbers e.g. next ones p = 1 , q = 3 --> R = 30 + {60*3/(1+3)} --> R = 30 + 180/4 --> R = 30 + 45 --> R = 75 and it is one of the choices, which is D

Or another simple quick way can be by just plugging in the numbers directly into the equation.

R = p/(p+q) * 30 + q/(p+q) * 90 --> as p<q, let's try p = 1 & q = 2 --> R = 1/(1+2) * 30 + 2/(1+2) * 90 = R = 1/3 * 30 + 2/3 * 90 --> R = 10 + 60 --> R = 70 not one of the choices and also all the choices with less than 70 eliminated and we are left with D & E....
This time with p = 1 & q = 3 --> R = p/(p+q) * 30 + q/(p+q) * 90 --> R = 1/(1+3) * 30 + 3/(1+3) * 90 --> R = 1/4 * 30 + 3/4 * 90 --> R = 1/4 (30 + 3 * 90) --> R = 1/4 (30 + 3 * 90) --> R = 1/4 (30 + 270) --> R = 1/4 (300) --> R = 75 ... matching choice D

And, the mistake I did in a hurry was that I forgot 30 in here 30 + {60q/(p+q)} and just went with plugging in the numbers because of which went for 45, which is B but of course wrong. So, don't get excited that it seems easy and may end up getting it wrong in a hurry.
User avatar
HMC
User avatar
Joined: 21 Jun 2016
Last visit: 06 Dec 2019
Posts: 58
Own Kudos:
26
Given Kudos: 9
Location: India
Posts: 58
Kudos: 26
If P, Q and R are Positive numbers - Which "Can" be the value of R? 27 Jul 2016, 05:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Atifs- With P = 1 and Q =2; You arrived at R =70, But how R cannot be less than 70?
P,Q, R - are just positive - they may not be integers.
User avatar
AtifS
User avatar
Joined: 20 Jan 2010
Last visit: 04 Jan 2017
Posts: 217
Own Kudos:
464
Given Kudos: 260
Status:Not afraid of failures, disappointments, and falls.
Concentration: Technology, Entrepreneurship
Schools: Haas '19 Darden '19 INSEAD Jan '19 Stanford '19 Anderson '19 HBS '19
WE:Operations (Telecommunications)
Schools: Haas '19 Darden '19 INSEAD Jan '19 Stanford '19 Anderson '19 HBS '19
Posts: 217
Kudos: 464
If P, Q and R are Positive numbers - Which "Can" be the value of R? 27 Jul 2016, 06:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HMC
Atifs- With P = 1 and Q =2; You arrived at R =70, But how R cannot be less than 70?
P,Q, R - are just positive - they may not be integers.

Yeah, you are right, they can be fraction numbers too. A bit naive of me :|
avatar
fireagablast
avatar
Joined: 30 Jun 2019
Last visit: 17 Aug 2021
Posts: 267
Own Kudos:
100
 []
Given Kudos: 8
Posts: 267
Kudos: 100
 []
If P, Q and R are Positive numbers - Which "Can" be the value of R? 20 Mar 2020, 16:27
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Question is tricky because it asks about R, but really you are looking at a soltion that fits the condition of Q and P.
30(p+3q)/(p+q) = R

r=75
75/30 = 5/2
(p+3q)/(p+q) = 5/2
5p+5q = 2p+6q

3p=q --> fits the condition that q>p
Moderator:
Bunuel
Math Expert
97877 posts