BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Problem in the Problem

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Senior | Next Rank: 100 Posts
Posts: 46
Joined: Mon Jun 18, 2012 10:32 pmFollowed by: 1 member
Thanked: 1 times
by smagish » Sun Jul 29, 2012 1:58 am
If x, y, and k are positive numbers such that (x)10/(x+y) + (y)20/(x+y) = k and if x < y, which of the following could be the value of k?

A. 10
B. 12
C. 15
D. 18
E. 30

I doubt the question to be erroneous....any thoughts

Thanks in advance:)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 210
Joined: Thu Mar 08, 2012 11:24 pmFollowed by: 3 members
Thanked: 62 times

by niketdoshi123 » Sun Jul 29, 2012 3:07 am
smagish wrote:If x, y, and k are positive numbers such that (x)10/(x+y) + (y)20/(x+y) = k and if x < y, which of the following could be the value of k?

A. 10
B. 12
C. 15
D. 18
E. 30
x, y, & k are positive numbers
x < y
Simplifying the given equation
(10x + 20y) = k(x+y)

Let plug in the value of k
We will start with option C as the options are in increasing order
Substituting k=15 in the equation

10x + 20y = 15x + 15y
=>5y = 5x => y = x but we know that x<y so eliminate option C. Also the value of k<15 will give us the inequality x>y, therefore eliminate options A and B.

Check for option E
k= 30

10x + 20y = 30x + 30y
=> -10y = 20x => y = -2x but we know that x and y both are positive. Hence eliminate option E

We are left with option D, which is the correct answer.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
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 » Sun Jul 29, 2012 8:18 pm
smagish wrote:If x, y, and k are positive numbers such that (x)10/(x+y) + (y)20/(x+y) = k and if x < y, which of the following could be the value of k?

A. 10
B. 12
C. 15
D. 18
E. 30

I doubt the question to be erroneous....any thoughts

Thanks in advance:)
(x/(x + y))(10) + (y/(x + y))(20) = k and x < y
10x + 20y = k(x + y)
x(10 - k) = y(k - 20)
y/x = (10 - k)/(k - 20) and we know y > x or y/x > 0

So, 15 < k < 20 implies k = 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/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Fri Jun 08, 2012 7:12 am
Thanked: 1 times

by sanrisenew » Tue Jul 31, 2012 2:39 am
10x/(x+y) + 20y/(x+y) = K


(10x+20y)/(x+y) =K

(10(x+y) + 10y)/(x+y) = k

10 + 10*y/(x+y) = K

Now, second term on LHS is less than 10 therefore , 30 is out
y/(x+y) can't be less than 1/2 as x<y therefore only option left is 18.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1