A certain smoothie A is three-fifths blueberries and 40%

The question was how much A is of the entire smoothie. To get there you divide A by the total batch.

A+B = total

A/(A+B) = Percentage of A in the total batch.

I solved this using alligation method as follows:

So, total = 15, contribution from A = 5; So 5/15 * 100 = 33.33 %
Answer = B

A is 40% raspberries;
B is 25% raspberries.
A and B is 30% raspberries;

30% raspberries in the mixed smoothie of A and B come from 40% raspberries in A and 25% raspberries in B, thus:

0.3(A+B)=0.4A+0.25B --> 0.1A=0.05B --> A/B=1/2 --> A/(A+B)=1/3.

Answer: B.

I understood everything except that step in red.

HI All,

In these sorts of scenarios, when you're not given a specific amount of the items involved (in this case, Smoothie A and Smoothie B), you can TEST VALUES and use real numbers to answer the question.

Here, we know:
Smoothie A is 40% raspberries
Smoothie B is 25% raspberries

We want to mix some of each and end up with a 30% raspberry mixture

Here's how to TEST VALUES:

Lets's say we have 10oz. of Smoothie A...
10(40%) = 4 oz. raspberries

Now, we can calculate how much Smoothie B we need by using the Weighted Average Formula:

Let's say we have Xoz. of Smoothie B...
X(25%) = .25X oz. raspberries

Rasp/All = (4+.25X)/(10+X) = .3

4+.25X = 3 + .3X
1 = .05X
20 = X

This means that we would need 20 ounces of Smoothie B to be mixed with 10 ounces of Smoothie A to end up with a 30% raspberry mix at the end. The question asks what percent of the mixture "belongs to Smoothie A"

A/All = 10/30 = 1/3 = 33.33%

Final Answer:

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

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.