Percent of the combined mixture that is dry fruits

Question

Hello,

Can you please help me with this :

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?

OA: [spoiler]23.33%[/spoiler]

I tried to solve as follows:

S:
N--------N+DF-------DF
30%----------------70%

J:
N--------N+CC-------CC
60%----------------40%

Since the combined mixture contains 50% nuts, the other 50% is dry fruits plus chocolate chips
S+J:
DF-------DF+CC------CC
70%-------50%---------40%

DF/CC = 10/20 = 1/2

I wasn't sure though if is correct to set up the ratio this way. Can you please help?

Thanks,
Sri

GMATGuruNY · Answer

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%

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

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 J on the ends and the percentage for the mixture in the middle.
S 30%-----------50%-----------60% W

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 ratio 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 pounds and J = 200 pounds, for a total of 300 pounds.
Since 70% of Sue's mix is dried fruit, the amount of dried fruit = .7(100) = 70 pounds.
Thus:
Dried fruit percentage = (dried fruit)/(total) * 100 = 70/300 * 100 = 70/3 = 23.33%.

The correct answer is B.

For two similar problems, check here:

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

Rich.C@EMPOWERgmat.com · Answer

Hi Sri,

This question can also be solved with a bit of algebra:

Sue's Mix: 30% nuts and 70% dried fruit
Jane's Mix: 60% nuts and 40% chocolate

Combined mix is 50% nuts…so we can create the follow equation:

X = number of servings of Sue's Mix
Y = number of servings of Jane's Mix

(.3X + .6Y)/(X + Y) = .5

.3X + .6Y = .5X + .5Y

.1Y = .2X

Y = 2X

This means that the mixture is "1 part" Sue's Mix and "2 parts" Jane's Mix, with a Total of 3 parts.

The question asks what percent of the Total Mix is dried fruit….

1(.7)/(1+2) = .7/3

Since .75/3 = 25%…

.7/3 has to be a little less than 25%

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

Percent of the combined mixture that is dry fruits

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER