A container holding 12 ounces of a solution that is 1

Hi All,

We're told that a container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water. We're asked for the ratio of alcohol to water in the resulting solution.

Since this prompt gives us all of the numbers to calculate the answer, the easiest way for most people to approach the prompt is to just 'do the math.' That having been said, there are some patterns in this question that you can use to get the correct answer another way (and on versions of this question that are MUCH harder). The first solution is 1 part alcohol to 2 parts water, so it is 1/3 alcohol; the second solution is 1 part alcohol to 3 parts water, so it's 1/4 alcohol. When we mix the two solutions, the resulting solution will have an alcohol percentage that is BETWEEN 1/4 (25%) and 1/3 (33 1/3%). In addition, since there is MORE of the 1/3 solution, that percentage will be CLOSER to 1/3 than it is to 1/4...

The answers are written in alcohol:water format, but we can easily convert each to alcohol:everything

Answer A) 2:5 --> 2/7 = about 28% (too small; closer to 25%)
Answer B) 3:7 --> 3/10 = 30% (looks good)
Answer C) 3:5 --> 3/8 = 37.5% (too big)
Answer D) 4:7 --> 4/11 = greater than 1/3 (too big)
Answer E) 7:3 --> 7/10 = 70% (too big)

Final Answer: B

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

BTGmoderatorLU wrote:A container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water. What is the ratio of alcohol to water in the resulting solution?

A. 2:5
B. 3:7
C. 3:5
D. 4:7
E. 7:3

The ratio of alcohol to water in the first solution is 1 : 2, or 1x : 2x. We can can create the equation:

x + 2x = 12

3x = 12

x = 4

So the first solution has 4 ounces of alcohol and 8 ounces of water.

The ratio of alcohol to water in the second solution is 1 : 3, or 1y : 3y. We can create the equation for the second solution:

y + 3y = 8

4y = 8

y = 2

So the second solution has 2 ounces of alcohol and 6 ounces of water.

So the ratio of alcohol to water in the mixed solution is 6/14 = 3/7.

Answer: B