BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Percent of the combined mixture that is dry fruits

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pm
Thanked: 11 times
Followed by:8 members

Percent of the combined mixture that is dry fruits

by gmattesttaker2 » Thu May 29, 2014 6:23 pm
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
Top
Source: — Problem Solving |
User avatar
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

by GMATGuruNY » Thu May 29, 2014 7:03 pm
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
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Thu May 29, 2014 9:16 pm
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]
Image
Top
Post new topic Post Reply
• Page 1 of 1