M07-28

Official Solution:

Lemonade A has a lemon acid to water ratio of 1:4, and Lemonade B has a lemon acid to water ratio of 1:5. In a mixture combining the two lemonades, the lemon acid to water ratio is 9:41. What is the ratio of the amount of Lemonade A to the amount of Lemonade B in this combined mixture?

A. 1:3
B. 16:25
C. 2:3
D. 3:4
E. 3:2


Assuming \(x\) amounts of Lemonade A and \(y\) amounts of Lemonade B were mixed, we can calculate the amount of lemon acid in each lemonade and in the combined mixture.

The amount of lemon acid in \(x\) amounts of Lemonade A is (lemon acid)/(total) = 1/(1 + 4) = 1/5 of \(x\).

The amount of lemon acid in \(x\) amounts of Lemonade A is (lemon acid)/(total) = 1/(1 + 4) = 1/5 of \(x\).

The amount of lemon acid in \(x+y\) amounts of the combined mixture is (lemon acid)/(total) = 9/(9 + 41) = 9/50 of \(x+y\).

We can equate the amounts of lemon acid in the lemonades and the combined mixture to obtain: \(\frac{1}{5}*x + \frac{1}{6}*y = \frac{9}{50}*(x+y)\)

Multiplying both sides by the least common multiple of 4, 6, and 50, which is 150, we get: \(30x +25y = 27(x + y)\). This simplifies to \(3x = 2y\), giving \(x:y=2:3\)


Answer: C
_________________

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
_________________

gmatophobia

can it be done with allegation diagram method ?

AnujL - Yes! it can be

Lemonade A has one part of lemon acid to 4 parts of water. So the ratio of acid to the liquid = \(\frac{1}{5}\)

Lemonade B has one part of lemon acid to 5 parts of water. So the ratio of acid to the liquid = \(\frac{1}{6}\)

The mixture has nine parts of lemon acid to 41 parts of water. So the ratio of acid to the liquid = \(\frac{9}{50}\)

Now, we can set up the diagram as shown below and find the ratio -



Option B

_________________

Hi Bunuel,

Why cant we consider A = 1/4 and B = 1/5

1/5----9/41----1/4

But Im getting the anwer as 4:5

Why do we need to convert it to lemonade/total

That's how allegation method works. Check the links below:

18. Mixture Problems

• Theory
  Weighted Average and Mixture Problems on the GMAT
  Tips and Tricks: Mixtures
  
  • Questions
    DS Questions
    PS Questions

For more check Ultimate GMAT Quantitative Megathread

_________________