A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?
A. 40%
B. 50%
C. 63%
D. 64%
E. 68
OA is B
What could be the correct answer to this? An Expert contribution will be appreciated.
Percents
This topic has expert replies
-
- Moderator
- Posts: 772
- Joined: Wed Aug 30, 2017 6:29 pm
- Followed by:6 members
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
ASIDE: We can eliminate C, D and E immediately (without performing any calculations).Roland2rule wrote:A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?
A. 40%
B. 50%
C. 63%
D. 64%
E. 68
Here's why: If we begin with a mixture that's 60% sugar and then we dilute it by adding water, the resulting mixture will have less than 60% sugar. So, eliminate C, D and E.
Okay, on to the solution.
7.5 liter mixture of water and sugar is 60% sugar.
60% of 7.5 liters is sugar
60% of 7.5 = 4.5, so the 4.5 mixture has 4.5 liters of sugar
1.5 liters of water is added
So, the volume of the new mixture is 9 liters.
Since no sugar was added, the volume of the sugar is still 4.5 liters
(4.5)/9 = 1/2 = 50%
So, the new mixture is [spoiler]50% sugar[/spoiler].
Answer: B
Cheers,
Brent
- EconomistGMATTutor
- GMAT Instructor
- Posts: 555
- Joined: Wed Oct 04, 2017 4:18 pm
- Thanked: 180 times
- Followed by:12 members
Hi Roland2rule,A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?
A. 40%
B. 50%
C. 63%
D. 64%
E. 68
OA is B
What could be the correct answer to this? An Expert contribution will be appreciated.
Let's take a look at your question.
7.5 litre mixture of water and sugar is 60% sugar.
Amount of sugar in 7.5 litre mixture is:
$$=7.5\times\frac{60}{100}$$
$$=\frac{75}{10}\times\frac{3}{5}$$
$$=\frac{15}{10}\times3$$
$$=\frac{45}{10}=4.5$$
It means, in 7.5 Litres of mixture of water and sugar, 4.5 litres is sugar and remaining 3 litres is water.
When 1.5 litres of water is added to the mixture,
Total amount of water in mixture = 3 + 1.5 = 4.5 litres.
Now the mixture has 4.5 litres of sugar and 4.5 litres of water.
Equal amount means that the mixture contains 50% sugar and 50% water.
Therefore, Option B is correct.
Hope it helps.
I am available if you'd like any follow up.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
- DavidG@VeritasPrep
- Legendary Member
- Posts: 2663
- Joined: Wed Jan 14, 2015 8:25 am
- Location: Boston, MA
- Thanked: 1153 times
- Followed by:128 members
- GMAT Score:770
An alternative approach: effectively, we're combining a 7.5 liter solution that's 60% sugar with a 1.5 liter solution (water) that's 0% sugar. If there's 5 times as much of the 60% solution as the 0% solution (7.5 is five times the value of 1.5), then we can represent the distances of the percent sugar of each solution from the total percent sugar as 5x and x.Roland2rule wrote:A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?
A. 40%
B. 50%
C. 63%
D. 64%
E. 68
OA is B
What could be the correct answer to this? An Expert contribution will be appreciated.
0-----------5x--------------Average---x---60
x + 5x = 60
6x = 60
x = 10
60 - 10 = 50. The answer is B
- 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
Alternate approach:Roland2rule wrote:A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?
A. 40%
B. 50%
C. 63%
D. 64%
E. 68
Since (added water)/(original volume) = (1.5)/(7.5) = 15/75 = 1/5, the total volume increases by 1/5.
Put another way, the resulting volume is 6/5 of the original volume.
As a result, the sugar percentage is multiplied by the RECIPROCAL of the fraction in red:
(60%)(5/6) = 50%.
The correct answer is B.
Another example:
A 100-liter mixture of water and sugar is 40% sugar. If 60 liters of water is added, approximately what is the % of the new mixture of sugar?
Since (added water)/(original volume) = 60/100 = 3/5, the total volume increases by 3/5.
Put another way, the resulting volume is 8/5 of the original volume.
As a result, the sugar percentage is multiplied by the RECIPROCAL of the fraction in red:
(40%)(5/8) = [spoiler]25%[/spoiler].
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