• PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep

Solution Y is 40 percent sugar by volume, and solution X...

This topic has 4 expert replies and 0 member replies

Solution Y is 40 percent sugar by volume, and solution X...

Post Thu Dec 07, 2017 10:40 am
Solution Y is 40 percent sugar by volume, and solution X is 20 percent sugar by volume. how many gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25 percent sugar by volume?

(A) 37.5
(B) 75
(C) 150
(D) 240
(E) 450

The OA is E.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Thu Dec 07, 2017 4:35 pm
Another approach would be finding the weighted average.

If X is 20% sugar, Y is 40% sugar, and X + Y = 25% sugar, then

.2x + .4y = .25(x + y)

.2x + .4y = .25x + .25y

.15y = .05x

3y = x

We were told y = 150, so x = 3y = 3*150 = 450.

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Thu Dec 07, 2017 4:34 pm
If we've got 150 gallons of solution Y, then 40% of 150, or 60 gallons of it are sugar.

From here, we're adding x gallons of Solution X. 20% of that is sugar, so

sugar / total = (60 + 0.2x) / (150 + x)

is our ratio.

We need that to equal 25%, or 1/4, so

(60 + 0.2x) / (150 + x) = 1/4

Then just cross multiply and solve for x:

4 * (60 + 0.2x) = 150 + x

240 + 0.8x = 150 + x

90 = 0.2x

450 = x

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

GMAT/MBA Expert

Post Thu Dec 07, 2017 12:37 pm
Hi swerve,

We're told that Solution Y is 40 percent sugar by volume, and solution X is 20 percent sugar by volume. We're asked for the number of gallons of Solution X that must be added to 150 gallons of Solution Y to create a solution that is 25 percent sugar by volume. This prompt is an example of a Weighted Average question - and while you can certainly solve it Algebraically, you can also TEST THE ANSWERS.

To start, IF we had an EQUAL amount of both Solutions in the mixture, then the average sugar percent would be (40+20)/2 = 30. That's not what we're after though - we want there to be a 25% average, so we clearly need MORE of Solution X than Solution. Y. We're told that there is 150 gallons of Solution Y in the mixture, so there has to be MORE than 150 gallons of Solution X. Thus, we can eliminate Answers A, B and C.

Let's TEST Answer E: 450 gallons

IF we have....
150 gallons of Solution Y and 450 gallons of Solution X, the ratio of Y:X is 1:3 and the average sugar content would be...

[(1)(40) + (3)(20)]/(1+3) =
[40 + 60]/4 =
100/4 = 25 percent

This matches what we were told, so this MUST be the answer.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Thu Dec 07, 2017 10:42 am
chaitanya.bhansali wrote:
Solution Y is 40 percent sugar by volume, and solution X is 20 percent sugar by volume. How many gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25 percent sugar by volume?

A) 37.5
B) 50
C) 62.5
D) 300
E) 450
When solving mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED.

Start with 150 gallons of solution that is 40% sugar:
ttp://postimg.org/image/m6rzscpk1/" target="_blank">
When we draw this with the ingredients separated, we see we have 60 gallons of sugar in the mixture.

Next, we'll let x = the number of gallons of solution X we need to add.
Since 20% of the solution X is sugar, we know that 0.2x = the volume of sugar in this solution:
ttp://postimg.org/image/nzuwgoaqp/" target="_blank">
At this point, we can ADD the two solutions (PART BY PART) to get the following volumes:
ttp://postimg.org/image/nbm1xqc0x/" target="_blank">
Since the resulting solution is 25% sugar (i.e., 25/100 of the solution is sugar), we can write the following equation:
(60 + 0.2x)/(150 + x) = 25/100
Simplify to get: (60 + 0.2x)/(150 + x) = 1/4
Cross multiply to get: 4(60 + 0.2x) = 1(150 + x)
Expand: 240 + 0.8x = 150 + x
Rearrange: 90 = 0.2x
Solve: x = 450

Answer: E

Cheers,
Brent

Here are some additional mixture questions to practice with:
http://www.beatthegmat.com/liters-of-mixture-x-in-the-50-mixture-t271387.html
http://www.beatthegmat.com/percentage-mixture-t268631.html
http://www.beatthegmat.com/rodrick-mixes-a-martini-that-has-a-volume-of-n-ounces-havi-t270387.html
http://www.beatthegmat.com/mixure-problem-quite-confusing-t261767.html
http://www.beatthegmat.com/mixture-ratio-problem-2-t191643.html

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

Best Conversation Starters

1 Roland2rule 181 topics
2 lheiannie07 110 topics
3 ardz24 60 topics
4 LUANDATO 55 topics
5 swerve 52 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

153 posts
2 image description GMATGuruNY

The Princeton Review Teacher

125 posts
3 image description Scott@TargetTestPrep

Target Test Prep

123 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

111 posts
5 image description EconomistGMATTutor

The Economist GMAT Tutor

83 posts
See More Top Beat The GMAT Experts