OG12 PS148

Expert replies

alex.gellatly: Master | Next Rank: 500 Posts; Posts: 435; Joined: Wed Nov 16, 2011 7:27 amFollowed by: 16 members; Thanked: 48 times

by alex.gellatly » Mon Sep 03, 2012 8:28 pm

OK I know this question has been posted several times on this site... but I still can't seem to understand the best approach for solving it.

If x, y, and k are positive numbers such that (x/x+y)(10)+(y/x+y)(20)=k and if x<y, which of the following could be the value of k?

10
12
15
18
30

Much thanks in advanced

A useful website I found that has every quant OG video explanation:

https://www.beatthegmat.com/useful-websi ... tml#475231

Like this post

Source: Beat The GMAT — Problem Solving | Mon Sep 03, 2012 8:28 pm

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Mon Sep 03, 2012 9:48 pm

Alex - Here it goes.

(x/x+y)(10) + (y/x+y)(20) = k
(x/x+y)(10) + (y/x+y)(10) + (y/x+y)(10) = k - Splitting (y/x+y)(20) into (y/x+y)(10) + (y/x+y)(10).
[(x+y)/(x+y)]*(10) + (y/x+y)(10) = k - Adding (x/x+y)(10) + (y/x+y)(10), we get [(x+y)/(x+y)]*(10).
10 + (y/x+y)(10) = k - Dividing numerator and denominator with (x+y), [(x+y)/(x+y)]*(10) = 10.

A)10

10 + (y/x+y)(10) = k = 10, then
10 + (y/x+y)(10) = 10
(y/(x+y))(10) = 0
y = 0. BUT y is a positive number (From the question). So, answer choice A is incorrect.

B)12

10 + (y/x+y)(10) = k = 12, then
(y/(x+y))*(10) = 2
10*y = 2*(x+y)
10y = 2x + 2y
8y = 2x
x = 4y. Since x and y are positive numbers and x = 4y, x is greater than y. BUT x<y(from the question).
So, answer choice B is incorrect.

C)15

10 + (y/x+y)(10) = k = 15, then
(y/(x+y))*(10) = 5
10*y = 5*(x+y)
10y = 5x + 5y
5y = 5x
y = x.
BUT x<y(From the question). So, answer choice C is incorrect.

D)18

10 + (y/x+y)(10) = k = 18, then
(y/(x+y))*(10) = 8
10*y = 8*(x+y)
10y = 8x + 8y
2y = 8x
y = 4x. x<y(From the question). So, answer choice D is correct.

E)30

10 + (y/x+y)(10) = k = 30, then
(y/(x+y))*(10) = 20
10*y = 20*(x+y)
10y = 20x + 20y
-10y = 20x
y = -2x.
If x is positive, then y is negative and If x is negative, then y is positive. BUT x, y, and k are positive numbers(From the question). So, answer choice D is incorrect.

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/

Like this post

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Sep 04, 2012 12:08 am

alex.gellatly wrote:OK I know this question has been posted several times on this site... but I still can't seem to understand the best approach for solving it.

If x, y, and k are positive numbers such that (x/x+y)(10)+(y/x+y)(20)=k and if x<y, which of the following could be the value of k?

10
12
15
18
30

Much thanks in advanced

We have 10x/(x+y) + 10y/(x+y) + 10y/(x+y) = k.
10 + 10y/(x+y) = k.
Now it is given that x < y.
x + y < 2y.
y/(x + y) > 1/2.
10y/(x + y) > 5.
10 + 10y/(x + y) > 15.
Also since both x and y are positive, y/(x+y) < 1.
10 + 10y/(x + y) < 20.
Therefore 15 < k < 20.
The only possible value of k is 18.

The correct answer is D.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review