How many ounces of water must be added to 10 ounces of 3 % alcohol and waer solution to reduce the solution to 1 % alcohol.
A)5
B)10
C)15
D)20
E)30
How many ounces of water must be added to 10 ounces of 3 %
This topic has expert replies
- AbhishekRyu
- Junior | Next Rank: 30 Posts
- Posts: 11
- Joined: Tue Aug 01, 2017 9:51 am
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
The original solution contains 10 ouncesAbhishekRyu wrote:How many ounces of water must be added to 10 ounces of 3 % alcohol and waer solution to reduce the solution to 1 % alcohol.
A)5
B)10
C)15
D)20
E)30
3% of that is alcohol
3% of 10 = 0.3
So, the original solution contains 0.3 ounces of alcohol
Let x = the amount of water (in ounces) that must be added
So, the volume of the RESULTING solution = 10 + x ounces
IMPORTANT: Since we're adding water only, the volume of alcohol does not change.
In other words, there are 0.3 ounces of alcohol in the RESULTING solution
We want the RESULTING solution to be 1% alcohol
In other words: (volume of alcohol in solution)/(total volume of solution) = 1/100
Rewrite as: 0.3 /(10 + x) = 1/100
Multiply both sides by (10 + x) to get: 0.3 = (10 + x)/100
Multiply both sides by 100 to get: 30 = 10 + x
Solve: x = 20
Answer: D
Cheers,
Brent
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Alcohol percentage in the original solution: 3%.AbhishekRyu wrote:How many ounces of water must be added to 10 ounces of 3 % alcohol and water solution to reduce the solution to 1% alcohol.
A)5
B)10
C)15
D)20
E)30
Alcohol percentage in the added water: 0%.
Alcohol percentage in the mixture: 1%.
Let S = the original solution and W = the added water.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with the percentages for S and W (3% and 0%) on the ends and the percentage for the mixture (1%) in the middle.
S 3%----------1%-----------0% W
Step 2: Calculate the distances between the percentages.
S 3%----2-----1%----1-----0% W
Step 3: Determine the ratio in the mixture.
The ratio of original solution to added water is equal to the RECIPROCAL of the distances in red.
S:W = 1:2 = 10:20.
The resulting ratio indicates that the 10 ounces of original solution must be combined with 20 ounces of water.
The correct answer is D.
For two similar problems, check here:
https://www.beatthegmat.com/ratios-frac ... 15365.html
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
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
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Initially, we have 0.03 x 10 = 0.3 ounces of alcohol and 9.7 ounces of water. To reduce the solution to 1% alcohol:AbhishekRyu wrote:How many ounces of water must be added to 10 ounces of 3 % alcohol and waer solution to reduce the solution to 1 % alcohol.
A)5
B)10
C)15
D)20
E)30
0.3/(10 + w) = 1/100
30 = 10 + w
20 = w
Alternate Solution:
To 10 ounces of 3% alcohol we will add x ounces of water (0% alcohol) to yield (x + 10) ounces of 1% alcohol. Changing the percents to decimals, we can express this in an equation as:
0.03(10) + 0.0(x) = 0.01(x + 10)
0.3 + 0 = 0.01x + 0.1
0.2 = 0.01x
20 = x
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews