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

I misread the question, Again!! Nyways another method
40% 50%
\ /
50%
/ \
100% 10%

so 50/10 = 15-x/x => x =2.5 cups

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Hope it helps.

1. In 15 cups the proper mix should be 50% melted chocolate and 50% raspberry puree but the actual mix made was 40% melted chocolate and 60% raspberry puree.

2. Raspberry puree should be 10% less and melted chocolate should be 10% more in the mixture. 10% is equal to 1.5 cups i.e., you need to have the net effect of taking 1.5 cups of raspberry puree out of the mixture and adding 1.5 cups of melted chocolate to the mixture.

3.The net effect of taking out 1 cup of mixture and replacing it with 1 cup of melted chocolate is that of taking out 0.6 cup of raspberry puree and adding 0.6 cup of melted chocolate.

4. So to achieve the desired net effect as in (2) we need to take out 1.5/0.6 i.e., 2.5 cups of the mixture and replace it with the same amount of melted chocolate.

The answer is therefore 2.5 cups.

Conentrating only on chocolate. Assuming that one would need to replace x cups of 40% chocolate by 100% chocolate, then-

(15-x)*(50-40)=x*(100-50),

i.e., product of distances (here the number of cups) from the mean concentration (i.e., 50%) of both the mixtures, i.e., the original mixture of 40% concentration of chocolate and pure chocolate respectively would be equal.
Simplifying, 15*10=60x. Hence, x=2.5 cups.

I just used quick math and started with C)

removing 3 cups, 60% of which is rasp, so you're removing 1.8, leaving you with 7.2 cups, and the remaining 1.2 comes from choco, leaving you with 4.8, adding 3 back in, you end up with too much choco, so it must be a or b. with b, you remove 2.5, 60% of which is rasp, or 1.5, leaving you with 7.5, and the remaining 1 comes from choco, leaving you with 5. Add 2.5 pure choco you get 7.5/7.5, so B) is the answer.

I think sometimes in the time time-span it would take to read, comprehend, figure out a formula, write it down and solve, you could have easily just plugged in the numbers. Remember, the GMAT doesn't know/care if you solved via basic plug-in math like I use, or some elegant formula. All that matters is if you got it correct.

Remember he is replacing the mixture by pure chocolate so with every cup X of the mixture he replaces he will pour x cups of pure chocolate. So we have:

6+x-2/5x = 9-3/5x
x=2.5

B

Hope it helps
Cheers!
J

Using the same method as SwarnaTestprep, I tried solving this problem using a table. You might find it easy to visualize what is going on when pure/impure cups of the ingredients are added or removed.

s1 0.4*15=6 cups, element 1 and 0.6*15=9 cups, element 2
s2 Remove x cups of the mix i.e., -0.4x cups element 1 and -0.6x cups element 2
s3 Add x cups element 1

The desired ratio of the elements is 1:1

Thus (6 - 0.4x +x) / (9 - 0.6x) = 1/1
=> x=2.5 cups

Chocolate ............. Raspberry ............ Total

6 .............................. 9 ........................ 15

Say "x" quantity is removed; New Equation is..

\(6 - \frac{6x}{15}\) .................. \(9-\frac{9x}{15}\) ..................... 15-x

Whatever the quantity removed, same amount of chocolate is added

\(6 - \frac{6x}{15} + x\) ............... \(9 - \frac{9x}{15}\) .................. 15 - x + x

Addition should be 50% of the total

Equation can be setup in 2 ways:

\(6 - \frac{6x}{15} + x = \frac{50}{100} * 15\) ................. (1)

OR

\(9 - \frac{9x}{15} = \frac{50}{100} * 15\) ................... (2)

Will got with (2) as it has variable only on one side (Minimal Calculations)

\(\frac{9x}{15} = 7.5\)

x = 2.5

Answer = B

I got this wrong, but I definitely understand it.

I think this way is the easiest to think about solving the problem. We need to end up with equal parts of two ingredients. In 15 cups, we need 7.5 cups of each ingredient. So, that means, taking out 1.5 of 9 total cups of the raspberry puree. Let's just compute how many total cups should be removed: 1.5/9 = x/15 or EVEN EASIER: 1/6 = x/15 --> x = 2.5

The best formula ever to solve most of the REMOVE AND REPLACE mixture questions=

Suppose a container contains x of liquid from which y units are taken out and replaced by water.

After n operations, the quantity of pure liquid = \(x ( 1- \frac{y}{x})^n\)

Lets use it here =

\(\frac{1}{2}* 15= 7.5\) which is a desired value.

Hence,

\(7.5 = 9 ( 1 - \frac{x}{15})^1\)

\(\frac{5}{6}= \frac{15-x}{15}\)

\(6x = 15\)

\(x = 2.5\)

P.S = You can use 6 as well for chocolate sauce in this formula.


Please Consider KUDOS if my post helped

Hi,
I was with you until " final number of cups of choc =\(6-0.4x+x\)"


After I came up with 6 and 9, i proceeded to divide the options in half. What I mean is, for option B, 2.5 -- if we removed 2.5, that means that we would remove half of the 2.5 = 1.25 of chocolate and 1.25 of puree. I'm not sure why you removed 40%(although I can see that 40% represents the chocolate percent). Logically, if we remove the sauce, wouldn't we remove equal parts of puree and equal parts of chocolate?

Hi, There! I guess I'm a few months too late on this response, but I'll try to give it a go.

When we remove cups of the sauce, we're removing parts of both chocolate and puree --- according to their respective percentages.

In this case: we have 15 cups of sauce. The prompt asks us to remove "X" amount of cups from the sauce, and add the same "X" amount of chocolate - to give us an equal 7.5/7.5 split.
We're not splitting the "X" amount.

For Choice B, if we take 2.5 out of 15 ... we have 12.5 cups of Sauce: giving us 5 cups of Chocolate and 7.5 cups of Puree (since we have to take 40% choc. and 60% Puree from the sauce)
Now, adding the same amount, 2.5 back into the Chocolate, we have the perfect split: 7.5/7.5 ... Hence, B is correct.

Now, how did we get there through the method you tried to follow?

First of all, let's think logically: we have 15 cups of Sauce, broken down to as you pointed out, 6 Chocolate and 9 Puree.
Focus only on the Chocolate. We need to raise its initial value UP to 7.5 by removing cups of the sauce, and replacing the SAME AMOUNT with cups of chocolate.

Now, to get 7.5, we need to remove "X" amount of the 15 cups of sauce and MULTIPLY that value by 40% --- giving us the chocolate value of the "reduced" sauce value.
Just like we earlier with Choice B: (15-2.5)(2/5) = 5

Then, we need to add the SAME "X" amount back into the chocolate. And, that's how we get this equation:
7.5 = 2/5 (15 - X) + X
7.5 = 6 - .4X + X
1.5 = .6X
X = 2.5

A good problem, for good practice. Hope that helped!

Different approach with Ratios that will help to answer with min calculation efforts.

Assume that x cups of the sauce is removed.

15 cups contain Choc & Rasp in the ratio 2 : 3 ---- (1)
15 - x cups contain Choc & Rasp in the ratio 2 : 3 ---- (2)
15 cups contain Choc & Rasp in the ratio 1 : 1 ---- (3) (After adding x cups of Choc)

Since to 15 - x cups of sauce we have added pure Choc, the amount of Rasp in 15 - x cups and the final 15 cups must be same.
Ensure that the ratios also reflect the same. So, in statement (3), change the ratio from 1 : 1 to 3 : 3

15 - x cups contain Choc & Rasp in the ratio 2 : 3 ---- (2)
15 cups contains Choc & Rasp in the ratio 3 : 3 ---- (3)

Now, from the above two ratios it is clear that Choc changed from 2 parts to 3 parts. So we have added 1 part of Choc which is the value of 'x'.
Also, from (3), we have 6 parts as 15 cups and hence 1 part must be 2.5 cups.

Hi all,
another approach to this Q, which could be slightly easier and less time consuming is..
15 cups with 40% of choc will mean there are 6 cups of choc..
what was it supposed to be.. 50% or .5*15=7.5 cups..
this is 1.5 cups short..

now he is to make up for this 1.5 cups..
if we take out one cup, which includes .4 choc and add one cup of pure choc, the final effect is addn of .6 cup of choc..

But we have to make up for 1.5 cups..
if .6 cup requires replacement of one cup,..
1.5 cup will require 1/.6 *1.5= 2.5 cups..
ans B

Can someone please explain if the quantity of Raspberry in the original (faulty) and the final mixture will remain the same? Since we are only adding Chocolate?

No. He is going to remove the sauce (mix of chocolate and raspberry) and then add more chocolate to it. So the initial amount of raspberry is not the same as the final amount. But after the removal process, he adds only chocolate so yes, in that step, the amount of raspberry does not change.

Check here for the complete solution: a-dessert-recipe-calls-for-50-melted-chocolate-and-50-rasp-158248.html#p1376400