Mixtures

Question

Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 50% nuts, what percent of the combined mixture is dried fruit?

A. 16.67%
B. 23.33%
C. 25%
D. 33.33%
E. 36.67%

[spoiler]OA: B[/spoiler]

Brent@GMATPrepNow · Answer

srcc25anu wrote:Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 50% nuts, what percent of the combined mixture is dried fruit?

A. 16.67%
B. 23.33%
C. 25%
D. 33.33%
E. 36.67%

[spoiler]OA: B[/spoiler]

Nut percentage in Sue's mix: 30%.
Nut percentage in Jane's mix: 60%.
Nut percentage in the mixture: 50%.

Let S = Sue's mix and J = Jane's mix.
To determine the ratio of S to J, use 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 J on the ends and the percentage for the mixture in the middle.
S 30%-----------50%-----------60% J

Step 2: Calculate the distances between the percentages.
S 30%----20----50%----10-----60% J

Step 3: Determine the ratio in the mixture.
The required rate of S to J is equal to the RECIPROCAL of the distances in red.
S:J = 10:20 = 1:2.

Since S:J = 1:2, let S = 100 units and J = 200 units, for a total of 300 units.
Since S is 70% dried fruit, the amount of dried fruit = .7S = .7(100) = 70 units.
Thus:
Percent of dried fruit = (dried fruit)/(total) * 100 = 70/300 *100 = 70/3 %.

The correct answer is B.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

Last edited by GMATGuruNY on Tue Jun 11, 2013 8:08 am, edited 1 time in total.

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GMATGuruNY · Answer

srcc25anu wrote:Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 50% nuts, what percent of the combined mixture is dried fruit?

A. 16.67%
B. 23.33%
C. 25%
D. 33.33%
E. 36.67%

[spoiler]OA: B[/spoiler]

Nut percentage in Sue's mix: 30%.
Nut percentage in Jane's mix: 60%.
Nut percentage in the mixture: 50%.

Let S = Sue's mix and J = Jane's mix.
To determine the ratio of S to J, use 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 J on the ends and the percentage for the mixture in the middle.
S 30%-----------50%-----------60% J

Step 2: Calculate the distances between the percentages.
S 30%----20----50%----10-----60% J

Step 3: Determine the ratio in the mixture.
The required rate of S to J is equal to the RECIPROCAL of the distances in red.
S:J = 10:20 = 1:2.

Since S:J = 1:2, let S = 100 units and J = 200 units, for a total of 300 units.
Since S is 70% dried fruit, the amount of dried fruit = .7S = .7(100) = 70 units.
Thus:
Percent of dried fruit = (dried fruit)/(total) * 100 = 70/300 *100 = 70/3 %.

The correct answer is B.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

Last edited by GMATGuruNY on Tue Jun 11, 2013 8:08 am, edited 1 time in total.

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

zazoz · Answer

I have a question about this kind of questions.

I personally solved this question by picking a smart number for Sue mix, and solve for other mix and reached to the answer. But here is my question, why cant we pick two smart numbers simultaneously? say, pick 100 for each of them? I know that lead to nowhere, but can you explain what is the logic behind this wrong approach?

thanks in advance

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