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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