• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

A solution consists of only water and alcohol such that the

This topic has 2 expert replies and 0 member replies

A solution consists of only water and alcohol such that the

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



e-GMAT

A solution consists of only water and alcohol such that the ratio of alcohol to water in the solution is 7:3. How much amount of water should be added to the solution (in milliliters) so that the resulting solution contains 60% alcohol?

1. Total quantity of the resulting solution is 350 milliliters.
2. The original solution contains 10.5 milliliters of alcohol for every 4.5 milliliters of water.

OA A.

  • +1 Upvote Post
  • Quote
  • Flag
Post
AAPL wrote:
e-GMAT

A solution consists of only water and alcohol such that the ratio of alcohol to water in the solution is 7:3. How much amount of water should be added to the solution (in milliliters) so that the resulting solution contains 60% alcohol?

1. Total quantity of the resulting solution is 350 milliliters.
2. The original solution contains 10.5 milliliters of alcohol for every 4.5 milliliters of water.
In the solution below, the unit considered is always milliliters.

Let´s use the k technique, one of the best tools of our method when dealing with ratios/proportions!

$$\left\{ \matrix{
\,{\rm{water}}\,\,\left( w \right)\,\,\, = \,\,3k \hfill \cr
\,{\rm{alcohol}}\,\,\left( a \right) = 7k \hfill \cr} \right.\,\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,\left\{ \matrix{
\,{\rm{water}}\,\,\left( w \right)\,\,\, = \,\,3k + x \hfill \cr
\,{\rm{alcohol}}\,\,\left( a \right) = 7k \hfill \cr} \right.\,\,\,\,\,\,\,{\rm{such}}\,\,{\rm{that}}\,\,\,\,\,\,{{7k} \over {10k + x}} = {3 \over 5}\,\,\,\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{{\rm{cross - multiply}}} \,\,\,\,\,\,5k = 3x\,\,\,\,\,\left( * \right)$$
$$? = x$$
$$\left( 1 \right)\,\,\,10k + x = 350\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,6x + x = 350\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\,\,$$
$$\left( 2 \right)\,\,{a \over w} = {{10.5} \over {4.5}}\,\,\left( { = {{105} \over {45}} = {7 \over 3}} \right)\,\,\,{\rm{already}}\,\,{\rm{known}}\,\,{\rm{pre - statements}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.\,\,\,$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

  • +1 Upvote Post
  • Quote
  • Flag
Post
AAPL wrote:
e-GMAT

A solution consists of only water and alcohol such that the ratio of alcohol to water in the solution is 7:3. How much amount of water should be added to the solution (in milliliters) so that the resulting solution contains 60% alcohol?

1. Total quantity of the resulting solution is 350 milliliters.
2. The original solution contains 10.5 milliliters of alcohol for every 4.5 milliliters of water.
We can let the amount of water to be added be w and the original amount of alcohol and water be 7x and 3x, respectively. We can create the equation:

(3x + w)/(7x + 3x + w) = 6/10

(3x + w)/(10x + w) = 3/5

5(3x + w) = 3(10x + w)

15x + 5w = 30x + 3w

2w = 15x

We need to determine the value of w. We see that w = 15x/2 or x = 2w/15. Therefore, if we know one of the two variables, then we know the other.

Statement One Only:

Total quantity of the resulting solution is 350 milliliters.

This means 10x + w = 350. Since x = 2w/15, we have:

10(2w/15) + w = 350

4w/3 + w = 350

4w + 3w = 1050

7w = 1050

w = 150

Statement one alone is sufficient.

Statement Two Only:

The original solution contains 10.5 milliliters of alcohol for every 4.5 milliliters of water.

This means original amount of alcohol and water are 10.5y and 4.5y, respectively. Therefore, we have:

7x = 10.5y and 3x = 4.5y

Either way, we have x = 1.5y. However, since y can be any positive number (for example, if y = 2, then x = 3 and if y = 4, then x = 6), we can’t determine a unique value of x, and therefore, we can’t determine the value of w. Statement two alone is not sufficient.

Answer: A

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag
  • 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • 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
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • 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
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • 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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT

Top First Responders*

1 fskilnik@GMATH 90 first replies
2 Brent@GMATPrepNow 52 first replies
3 Jay@ManhattanReview 45 first replies
4 GMATGuruNY 31 first replies
5 Rich.C@EMPOWERgma... 24 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

181 posts
2 image description Scott@TargetTestPrep

Target Test Prep

150 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

111 posts
4 image description Max@Math Revolution

Math Revolution

91 posts
5 image description Jay@ManhattanReview

Manhattan Review

78 posts
See More Top Beat The GMAT Experts