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A dessert recipe calls for 50% melted chocolate and 50% rasp

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A dessert recipe calls for 50% melted chocolate and 50% rasp

by hazelnut01 » Wed May 17, 2017 9:03 pm
A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?

A. 1.5
B. 2.5
C. 3
D. 4.5
E. 5

Source : Veritas
OA=B
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by GMATGuruNY » Thu May 18, 2017 2:40 am
ziyuenlau wrote:A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?

A. 1.5
B. 2.5
C. 3
D. 4.5
E. 5
Chocolate percentage in the incorrect sauce: 40%.
Chocolate percentage in the pure chocolate: 100%.
Chocolate percentage in the mixture: 50%.

Let I = the incorrect sauce and C = the pure chocolate.
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 I and C on the ends and the percentage for the mixture in the middle.
I 40%----------50%-----------100% C

Step 2: Calculate the distances between the percentages.
I 40%----10----50%----50-----100% C

Step 3: Determine the ratio in the mixture.
The ratio of I to C is equal to the RECIPROCAL of the distances in red.
I:C = 50:10 = 5:1.

Since I:C = (5 cups) : (1 cup), 1 of every 6 cups must be pure chocolate.
Thus:
Pure chocolate = (1/6)(15 cups) = 15/6 = 5/2 = 2.5 cups.

The correct answer is B.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html
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by GMATGuruNY » Thu May 18, 2017 2:53 am
ziyuenlau wrote:A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?

A. 1.5
B. 2.5
C. 3
D. 4.5
E. 5
An alternate approach is to PLUG IN THE ANSWERS.
When the correct answer choice is plugged in, 50% of the 15-cup recipe -- in other words, 7.5 cups -- will be chocolate.

Answer choice D: 4.5 cups pure chocolate, implying 10.5 cups incorrect sauce, for a total of 15 cups
Since 40% of the incorrect sauce is chocolate, amount of chocolate in the incorrect sauce = (0.4)(10.5) = 4.2 cups.
Total chocolate = (pure chocolate) + (chocolate in incorrect sauce) = 4.5 + 4.2 = 8.7 cups.
The total amount of chocolate is too great.
Thus, LESS pure chocolate is needed, implying that the correct answer must be SMALLER.
Eliminate D and E.

Answer choice B: 2.5 cups pure chocolate, implying 12.5 cups incorrect sauce, for a total of 15 cups
Since 40% of the incorrect sauce is chocolate, amount of chocolate in the incorrect sauce = (0.4)(12.5) = 5 cups.
Total chocolate = (pure chocolate) + (chocolate in incorrect sauce) = 2.5 + 5 = 7.5 cups.
Success!

The correct answer is B.
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by elias.latour.apex » Thu May 18, 2017 3:39 am
This problem is amenable to a parts solution.

We have 15 cups of 40% chocolate and 60% raspberry puree. This can be reduced to 2 parts chocolate to 3 parts raspberry in every cup.

Accordingly, in the 15 cups we have 30 parts of chocolate to 45 parts of raspberry, a difference of 15 parts.

Since each cup substituted removes 3 parts of raspberry and adds 3 parts of chocolate, each cup narrows the difference by 6 parts.

Thus, the answer is 15/6 = 5/2 = 2.5, which is answer choice (B).
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by Mo2men » Thu May 18, 2017 6:29 am
GMATGuruNY wrote:
ziyuenlau wrote:A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?

A. 1.5
B. 2.5
C. 3
D. 4.5
E. 5
Chocolate percentage in the incorrect sauce: 40%.
Chocolate percentage in the pure chocolate: 100%.
Chocolate percentage in the mixture: 50%.

Let I = the incorrect sauce and C = the pure chocolate.
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 I and C on the ends and the percentage for the mixture in the middle.
I 40%----------50%-----------100% C

Step 2: Calculate the distances between the percentages.
I 40%----10----50%----50-----100% C

Step 3: Determine the ratio in the mixture.
The ratio of I to C is equal to the RECIPROCAL of the distances in red.
I:C = 50:10 = 5:1.

Since I:C = (5 cups) : (1 cup), 1 of every 6 cups must be pure chocolate.
Thus:
Pure chocolate = (1/6)(15 cups) = 15/6 = 5/2 = 2.5 cups.

The correct answer is B.

For two similar problems, check here:

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

The prompt asks for correction through REMOVAL cups from Incorrect sauce.

What if the prompt asks to make correction through ADDING Pure Chocolate cups. how to deal then with this situation?

Thanks
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by GMATGuruNY » Thu May 18, 2017 6:35 am
Mo2men wrote:
Step 3: Determine the ratio in the mixture.
The ratio of I to C is equal to the RECIPROCAL of the distances in red.
I:C = 50:10 = 5:1.
Dear Mitch,

The prompt asks for correction through REMOVAL cups from Incorrect sauce.

What if the prompt asks to make correction through ADDING Pure Chocolate cups. how to deal then with this situation?

Thanks
Since I:C = 5:1 = 15:5, every 15 cups of incorrect sauce must be combined with 5 cups of pure chocolate.
Thus, 5 cups of pure chocolate would need to be added to the 15 cups of incorrect sauce.
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by [email protected] » Thu May 18, 2017 2:10 pm
Hi ziyuenlau,

This question can be solved by TESTing THE ANSWERS.

To start, we're told that 15 cups of 'sauce' are made up of 40% chocolate and 60% raspberry. This gives us...

Total = 15 cups
Choc = 40%(15) = 6 cups
Rasp = 60%(15) = 9 cups

We're told to remove a certain amount of the mixture and replace it with PURE chocolate, so that the mixture becomes a 50/50 chocolate/raspberry mix. In simple terms, we need the total amount of Chocolate to be 7.5 CUPS. We're asked for the number of cups of the mixture that would have to be replaced. Let's TEST THE ANSWERS.

While it's mathematically advantageous to TEST answer B or D first, Answer C seems like easier math...

IF... we remove 3 cups of sauce, those 3 cups are....
40%(3) = 1.2 cups Choc
60%(3) = 1.8 cups Rasp

The number of cups of Choc can be calculated by using the original number of cups (6), subtracting the amount removed when we remove the sauce (in this case, 1.2), then adding back the pure chocolate that replaces the removed sauce (in this case, 3) = 6 - 1.2 + 3 = 7.8 cups chocolate. This is TOO MUCH chocolate (we wanted it to be 7.5 cups), but it's fairly close, so we're likely looking for an answer that is CLOSE to 3....Let's TEST Answer B...

IF... we remove 2.5 cups of sauce, those 2.5 cups are....
40%(2.5) = 1 cup Choc
60%(2.5) = 1.5 cups Rasp

Choc = 6 - 1 + 2.5 = 7.5 cups chocolate. This is EXACTLY what we're looking for, so this MUST be the answer.

Final Answer: B

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Rich
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