PS Mixtures

[sreenunna]

According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce cans of the concentrate are required to prepate 200 6-ounce servings of orange juice?

A) 25
B) 34
C) 50
D) 67
E) 100

Official Answer is revealed later and the question is from GMAT official source

[GMATGuruNY]

According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce cans of the concentrate are required to prepate 200 6-ounce servings of orange juice?

A) 25
B) 34
C) 50
D) 67
E) 100

Official Answer is revealed later and the question is from GMAT official source

Total = 200 6-ounce servings = 200*6 = 1200 ounces.
Since each can = 12 ounces, the total = 1200/12 = 100 cans.
In these 100 cans of mixture, since concentrate:water = 1:3 and 1+3=4, concentrate/total = 1/4.
Thus, in the 100 cans of mixture, the number of cans of concentrate = (1/4)100 = 25.

The correct answer is A.

[Brent@GMATPrepNow]

According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce cans of the concentrate are required to prepate 200 6-ounce servings of orange juice?

A) 25
B) 34
C) 50
D) 67
E) 100

Here's a slightly different approach that uses equivalent ratios.

The first part tells that, for every 1 can of concentrate, we can make 4 cans of juice.
Let's be even more generic, for 1 volume of concentrate, we can make 4 volumes of juice.

Okay, now notice that we have a problem with the volume mismatch in the question. It involves 12-ounce cans of concentrate and 6-ounce servings.
So, let's reword the question. Instead of making 200 6-ounce servings of juice, let's make 100 12-ounce servings of juice. This is acceptable since we're still making the same amount of juice!

We're now asking, "How many 12-ounce cans of the concentrate are required to prepare 100 12-ounce serving of orange juice?

We'll solve this question using equivalent ratios.

(volume of concentrate)/(volume of juice): 1/4 = x/100

Solve for x to get [spoiler]x=25[/spoiler]
So, the answer is A

Cheers,
Brent