Percents

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pmFollowed by: 6 members

by BTGmoderatorRO » Fri Dec 29, 2017 9:25 am

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.

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Source: Beat The GMAT — Problem Solving | Fri Dec 29, 2017 9:25 am

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by Brent@GMATPrepNow » Fri Dec 29, 2017 12:48 pm

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

ASIDE: We can eliminate C, D and E immediately (without performing any calculations).
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

Brent Hanneson - Creator of GMATPrepNow.com

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Fri Dec 29, 2017 12:50 pm

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.

Hi Roland2rule,
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.

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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Tue Jan 02, 2018 4:55 pm

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.

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.

0-----------5x--------------Average---x---60

x + 5x = 60
6x = 60
x = 10
60 - 10 = 50. The answer is B

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GMATGuruNY: 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 » Tue Jan 02, 2018 11:03 pm

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

Alternate approach:

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].

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