Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.

See classes
Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

Newsweek Readers’ Choice Awards 2026 winner: Target Test Prep, #1 Test Prep

Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.

★★★★★5.0563 reviews
GMATLiveTeachStarts Nov 22
Josh Braslow, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Josh Braslow, 20+ years in test prep

Nov 22 · Josh Braslow
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemandStart anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

EXECUTIVE ASSESSMENT

with

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemandStart anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 563 reviewsTarget Test Prep

Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:

Expert replies
Post new topic Post Reply
Subscribe topic
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 138
Joined: Sat May 05, 2012 7:03 pm
Thanked: 1 times
by gmatter2012 » Sun Jul 08, 2012 9:54 pm
Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of X to Y is 5:4?

A. 6:1
B. 5:4
C. 20:7
D. 10:9
E. 14:11
Top
Join the discussion
Source: — Problem Solving |

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 08, 2012 10:10 pm
gmatter2012 wrote:Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of X to Y is 5:4?
Algebraic Approach:
Say, m volume of first mixture and n volumes of second mixture were mixed. We need to find m:n.

Amount of X in the new mixture = (3m/5 + 3n/7) = (21m + 15n)/35
Amount of Y in the new mixture = (2m/5 + 4n/7) = (14m + 20n)/35

So, [(21m + 15n)/35]/[(14m + 20n)/35] = 5/4
--> 4(21m + 15n) = 5(14m + 20n)
--> (84m + 60n) = (70m + 100n)
--> 14m = 40n
--> m/n = 40/14 = 20/7

The correct answer is C.
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
User avatar
Legendary Member
Posts: 520
Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members
Thanked: 339 times
GMAT Score:770

by eagleeye » Sun Jul 08, 2012 11:41 pm
gmatter2012 wrote:Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of X to Y is 5:4?
Let's assume that we mix amount a of 3:2 mixture and amount b of 3:4 mixture to get (a+b) of 5:4 mixture. We need to find a/b. Let's equate the amount of X in all of them.
Amount of X in 3:2 mixture = 3*a/5. Amount of X in b = 3*b/7. Amount in overall mixture = 5*(a+b)/9
Then 3a/5+3b/7 = 5(a+b)/9
=> 9* (21a+15b) = 35*5*(a+b)
=> 189a + 135b = 175a+175b
=> a(189-175) = b(175-135)
=> a*14 = b*40
=> a/b = 40/14 = 20/7
So we need to mix them in 20:7 ratio :)
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 141
Joined: Tue Oct 04, 2011 5:17 am
Thanked: 25 times

by coolhabhi » Sun Jul 08, 2012 11:45 pm
gmatter2012 wrote:Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of X to Y is 5:4?

A. 6:1
B. 5:4
C. 20:7
D. 10:9
E. 14:11
In first mixture, X = 3/5
In second mixture, X = 3/7
resultant mixture, X = 5/9
Use allegations rule.

3/7 3/5
5/9
(3/5)-(5/9) (5/9)-(3/7)
2/45 8/63

Mixture2 : Mixture1 = (2/45) : (8/63)
=>Mixture2 7
--------- = ---
Mixture1 20
=>M1 : M2 = 20 : 7
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 141
Joined: Tue Oct 04, 2011 5:17 am
Thanked: 25 times

by coolhabhi » Mon Jul 09, 2012 12:10 am
gmatter2012 wrote:Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of X to Y is 5:4?

A. 6:1
B. 5:4
C. 20:7
D. 10:9
E. 14:11
In first mixture, X = 3/5
In second mixture, X = 3/7
resultant mixture, X = 5/9
Use allegations rule.

3/7 3/5
5/9
(3/5)-(5/9) (5/9)-(3/7)
2/45 8/63

Mixture2 : Mixture1 = (2/45) : (8/63)
=>Mixture2 7
--------- = ---
Mixture1 20
=>M1 : M2 = 20 : 7
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 138
Joined: Sat May 05, 2012 7:03 pm
Thanked: 1 times

by gmatter2012 » Mon Jul 09, 2012 12:33 am
Anurag@Gurome wrote:
gmatter2012 wrote:Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of X to Y is 5:4?
Algebraic Approach:
Say, m volume of first mixture and n volumes of second mixture were mixed. We need to find m:n.

Amount of X in the new mixture = (3m/5 + 3n/7) = (21m + 15n)/35
Amount of Y in the new mixture = (2m/5 + 4n/7) = (14m + 20n)/35

So, [(21m + 15n)/35]/[(14m + 20n)/35] = 5/4
--> 4(21m + 15n) = 5(14m + 20n)
--> (84m + 60n) = (70m + 100n)
--> 14m = 40n
--> m/n = 40/14 = 20/7

The correct answer is C.

Anurag this method was awesome , using this I have solved another similar question using this same method

https://www.beatthegmat.com/two-alloys-a ... tml#485112

Thank you
Top
Join the discussion
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Mon Jul 09, 2012 3:01 am
gmatter2012 wrote:Two mixtures of X and Y have X and Y in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of X to Y is 5:4?

A. 6:1
B. 5:4
C. 20:7
D. 10:9
E. 14:11
The following approach is called alligation.
It's a very good way to handle MIXTURE PROBLEMS.

Let F = the first mixture and S = the second mixture.

Step 1: Convert the ratios to FRACTIONS.
F:
Since X:Y = 3:2, and 3+2=5, X/total = 3/5.
S:
Since X:Y = 3:4, and 3+4=7, X/total = 3/7.
New mixture:
Since X:Y = 5:4, and 5+4=9, X/total = 5/9.

Step 2: Put the fractions over a COMMON DENOMINATOR.
F = 3/5 = (3*7*9)/(5*7*9) = 189/(5*7*9).
S = 3/7 = (3*5*9)/(5*7*9) = 135/(5*7*9).
New = 5/9 = (5*5*7)/(5*7*9) = 175/(5*7*9).

Step 3: Plot the 3 numerators on a number line, with the two starting numerators (189 and 135) on the ends and the goal numerator (175) in the middle.
F(189)--------------------(175)--------S(135)

Step 4: Calculate the distances between the numerators.
F(189)----------14---------(175)----40----S(135)

Step 5: Determine the ratio in the mixture.
The ratio of F to S in the mixture is the RECIPROCAL of the distances in red.
F : S = 40 : 14 = 20:7.

The correct answer is C.

For two other problems that I solved with alligation, check here:

https://www.beatthegmat.com/ratios-fract ... tml#484583
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion