Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai

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?

16.67%
23.33%
25%
33.33%
36.67%

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

KarishmaB · Accepted Answer

Use scale method. First thing to do is to find out the ratio in which the two mixes were mixed together.

Sue's mix had 30% nuts and Jane's had 60%. Overall, it had 50% nuts

WSue/WJane = (60 - 50)/(50 - 30) = 1/2

So if Sue's mix was 100 gms (30 gm nuts, 70 gms dried fruit), it was mixed with 200 gms of Jane's mix. 
So out of 300 gms of total mix, there was 70 gms of dried fruit i.e. (70/300) * 100 = 23.33%

Answer (B)

PareshGmat · Answer

Let Sue's mix = a

Nuts  = \frac{30a}{100}

Dry fruit  = \frac{70a}{100}

Let Janes mix = b

Nuts  = \frac{60b}{100}

Chocolate  = \frac{40b}{100}

Combined mixture of Sue and Jane's trails mix contains 50% nuts

\frac{30a}{100} + \frac{60b}{100} = \frac{50}{100} (a+b)

3a + 6b = 5a + 5b

2a = b

It means quantity of Jane is twice that of Susan. Lets take numbers to solve this further

If Sue's mix = 10 gms, then Jane's mix = 20 Gms

Total = 10+20 = 30 Gms

Quantity of Dry fruits = 70% = 7 Gms

Percentage  = \frac{7}{30} * 100 = 23.33%

Answer = B

WoundedTiger · Answer

untitled.PNG Sol: Given that new mixture is 50 % nuts which is (50-30 =20) away from Sue's trail and (60-50=10) away from Jane's trail Therefore, the ratio of Sue and Jane's mixture will be 1:2. So if Sue's mixture is 100 gms then Jane's mixture will be 200 gms From the table we can see that DF is 70 gm of Sue's mixture which is nothing 70/300*100 = 23.33% Ans is A

PerfectScores · Answer

Using alligation:

30 %.................60 %

...............50 %

10......................20

1 : 2

Hence both the mixtures are mixed in 1 : 2.

Let us say 10 grams of Suel's and 20 grams of Jane

Dried Fruit = 7

Total = 30

Percentage= 7/30 = 23.33 %

If you want to learn alligation you can watch the video by clicking on the links in the signature.

TGC · Answer

Another Approach:

Whenever one part of the mixture is changed by mixing track that part. This is indirect approach which leads to same solution as through alligation.

Take X from 1 mixture
Take Y from 2 mixture

{0.3X + 0.6Y}/(X+Y) = 1/2

X:Y = 1:2

30+70+120+80=300

70/300

gracie · Answer

.3S+.6J=.5(S+J)
S/J=1/2
S/(S+J)=1/3
(1/3)(.7)=.2333=23.33%

ricardobs006 · Answer

I am using the following approach which I saw in similar problems but it seems that in no way it helps! Could anyone please tell what is wrong in the approach? Maybe I am committing a silly mistake.

N - F - Ch
30 70 0
60 0 40

Combining:

N F Ch
1800 4200 0
1800 0 1200
-----------------------
1800 4200 1200

Simplifying:

N F Ch
3 7 2

Asuming 100 g of total mixture:
12*x= 100 --> x= 100/12

Total g of F --> (100/12) * 7

The question ask for (F/total mixture). Hence:

(100/12)*7 / 100 = 7/12= 0.583 --> in percentage = 58.3%

Could you please tell? Thanks!

SamBoyle · Answer

The first thing you should notice is that the combined mixture is 50% and Sue is at 30%. We can quickly see what would happen if the mixture was 1/1. It would be 0.3 + 0.6 then divided by 2 or 45%.

In order to get to 50% we must have more of Jane's mixture then Sue. With this in mind, it will make it easier to solve. We are going to figure out the proportion of S mixture to J= jane mixture. In my chart I used N1=Sue mixture amount and N2= Jane

JeffTargetTestPrep · Answer

To start we can define a few variables:

x = the total amount of Sue’s trail mix, and y = the total amount of Jane’s trail mix

We are given that Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. We can represent this below:

Nuts in Sue’s trail mix = 0.3x

Dried fruit in Sue’s trail mix = 0.7x

Nuts in Jane’s trail mix = 0.6y

Chocolate chips in Jane’s trail mix = 0.4y

We are also given that when the two trail mixes are combined, the resulting trail mix will contain 50% nuts. Since nuts in Sue’s trail mix = 0.3x, nuts in Jane’s trail mix = 0.6y, and the total weight of the two trail mixes is x + y, we can create the following equation:

(0.3x + 0.6y)/(x + y) = 50% = 0.5

0.3x + 0.6y = 0.5x + 0.5y

0.1y = 0.2x

y = 2x

Now we can determine what percent of the combined mixture is dried fruit. Since only Sue’s mixture contains dried fruit, we know that the only dried fruit in the mixture is 0.7x. We also know that the total weight of the mixture is x + y, so we can create the following ratio:

0.7x/(x + y)

0.7x/(x + 2x)

0.7x / 3x

0.7/3 = 0.2333…

So, the combined trail mix contains approximately 23.33% dried fruit.

Answer: B

EMPOWERgmatRichC · Answer

Hi All,

This question can 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

jzqmah · Answer

Bunuel  Can you please link to similar questions? Thank you so much!

NinetyFour · Answer

IMO the best way to solve this question is to use allegation.

ratio of Sue : Jane's trail mix must be in a 1:2 ratio.

That means total will be 100% Sue and 200% Jane, total mixture is 300% original size.

Sue's mixture has 70% dried fruit so  \frac{70}{300} = 23.33%

GreenDot · Answer

Let Sue's mixture be x, and Jane's mixture be y.
Nuts %age => 0.3x+0.6y/(x+y) * 100 = 50
This simplifies into y=2x
Dry fruits %age => 0.7x/x+y * 100
=> 0.7x/3x * 100 = 23.33

Posted from my mobile device

dcummins · Answer

See image for  Step 1. 
Note: we assumed a total weight of 100 units for step 1.

Step 2 -   Determine the amount that Sue's mix contributes to final mix i.e. determine x

0.3x +0.6(100-x)= 50
0.3x+60-0.6x=50
-0.3x=-10
3x/10=10
3x=100
x=100/3 (this is the weight of Sue's mix)

Step 3  -  determine the amount of fruit  
Since we know the weight of Sue's mix, we can use the proportion given to us.
Fruit = 70%

7/10 * 100/3 
=70/3
=23 1/3

BrentGMATPrepNow · Answer

Let's say that the combined mixture weighs   100 pounds  . 
If the combined mix is 50% nuts, then there are  50  pounds of nuts in the combined mixture.

Let's let x = the # of pounds of Sue's trail mix
This means that   100  -x = the # of pounds of Jane's trail mix

My word equation:  (# of pounds of nuts in Sue's portion) + (# of pounds of nuts in Jane's portion) =   50 
In other words: (30% of x) + (60% of   100  -x) =  50 
Rewrite as: 0.3x + 0.6(  100  -x) =  50 
Expand: 0.3x + 60 - 0.6x =  50 
Simplify: -0.3x = -10
Solve: x = 10/0.3 = 100/3 =  33 1/3

In other words, the combined ( 100-pound ) mixture contains  33 1/3  pounds of Sue's trail mix.
If Sue's trail mix is 70% dried fruit, then the total weight of dried fruit = (0.7)( 33 1/3 ) = 23 1/3

So, of the  100 pounds  of combined mix, there are 23 1/3 pounds of dried fruit. 
In other words, 23 1/3% of the combined mixture is dried fruit?

Answer: B

Cheers,
Brent

Basshead · Answer

60 - 50 / 50 - 30 = 10/20 = 1/2

Therefore the combined mix is 33% Sue's mix and 66% Jane's mix.

Out of Sue's 33% mix, 70% is dried fruit.

Therefore 23.3% contains dried fruit. Answer is B.

ocelot22 · Answer

Lets let x = fraction of trail mix that is sues, and 1-x = fraction of trail mix that is janes, and we will convert everything to decimals in our final calculation

then 30X + 60(1-x) = 50. Everything in our equation is in terms of percents so looks good

so -30x = -10 and x = 1/3. So we then needs to take .33 of .7 which gives .2331, which is closest to B

OA is B

epsilon-delta · Answer

We have established that the ratio of Jane's trail mix (J) to Sue's trail mix (S) is 2:1.

Now, let's determine the overall composition of the combined mixture:

For nuts: Since Jane's mix has twice as many nuts as Sue's mix (60% vs. 30%), the overall nuts in the combined mixture will be weighted more toward Jane's mix. It will be more than 50%, but we can't determine the exact percentage with the given information.

For dried fruit: Since Sue's mix is 70% dried fruit (which is higher than Jane's mix), the overall dried fruit in the combined mixture will also be weighted more toward Sue's mix. It will be more than 50%, but we can't determine the exact percentage with the given information.

Given the information provided, we can conclude that the percent of the combined mixture that is dried fruit is more than 50%.

So, if the answer is indeed among the options given, then option (B) "23.33%" would be the closest approximation. However, it's important to note that we cannot calculate the exact percentage based on the information provided. If option (B) is considered the correct answer, it is an approximation.

wasario · Answer

As I like to do with ratio problems, I like to represent them as equations if possible because it makes it easier to visualize and solve. Firstly, we know the percentages of nuts in both the individual and the combined mixtures. Moreover, we also know that Sue's the only one who had any dried fruit. Thus, if we can figure out how much total amount we had from combining them, and then taking Sue's fruit amount from that, we will have the answer.

Let's say Sue's mixture amount is  s  and Jane's is  j . We can represent the nuts ratio as an equation:

\frac{.3s + .6j}{s+j} = 0.5

We can then do some variable manipulating to get the following:

.3s + .6j = .5s + .5j 
 .1j = .2s 
 j = 2s

Thus, we now know that Jane had twice as much trail mix as Sue. Therefore, we know that in terms of  s , the total amount of trail mix in the combined mixture was  s + 2s = 3s . And since we know that the dried fruit amount was  .7s , we can now construct our ratio of fruit to total as:

\frac{.7s}{3s} = \frac{.7}{3} = \frac{7}{30} = 0.233333... = 23.3333... %

Hence our answer is  B

Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai

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Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trai

Prep Toolkit

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