### But first, try solving this question:

If you mix a 200 liter solution of 7% alcohol and a 300 liter solution of 12% alcohol, what is the resulting concentration?

A. 6 %

B. 6.5%

C. 8%

D. 10%

E. 12.5%

**Think about it before you scroll down**

This is a weighted average GMAT type question. Traditionally you can determine the answer by using the simple formula: (200•7% + 300•12%)/(200+300) and get 10%, or you can quickly solve this problem remembering something very fundamental: the average of two quantities can never be more or less than either of these quantities, and must be between them. The new concentration we are trying to calculate is like the weighted average of either concentration. Like the average, the weighted average must lie between the two quantities, except that it will be closer to the concentration in higher quantity.

For example, the average of 123 and 134 cannot be more or less than either one and must be between them. This may be obvious in a simple situation, but harder to notice when mixtures or ratios are thrown into the problem.

In the case of the problem above, you can quickly eliminate all answer choices except C and D because only C and D lie within the range. Because there is more of the 12% solution, we know that the answer must be closer to 12% than 7%, leaving D as the possible answer. In this case, no calculations were even necessary.

Think of the GMAT as the simulation of small business situations in which you must consider all available information, including the possible solutions, and make a decision in a limited amount of time.

A more challenging application can be in more abstract situations in which one or two extra inference steps are required. Consider this problem:

In a classroom, some students are signed up for extra-curricular activities and some are not. Is the ratio of boys signed up to the extra-curricular activities to the boys who are not less than the ratio of the students signed up to extra-curricular activities to the students who are not?

(1) More than 2/3 of the boys are signed up for extra-curricular activities and more than 3/4 of the girls are not signed up for extra-curricular activities.

(2) The ratio of girls who are signed up for extra-curricular activities to girls who are not is less than that ratio for the whole class.

**Think about it before you scroll down**

This can also be thought of as the weighted average problem above. The ratio of students taking extra-curricular activities to students who are not can be thought of as a “concentration”, say 10% alcohol, only in this case it is an x% taking extra-curricular activities. This case is exactly the same.

From statement (1) we know that this concentration is less for the girls than for the boys (more than 3/4 not signed up therefore less than 1/4 signed up), hence, the average concentration for the whole class must be less than that for the boys. – This statement on its on is Sufficient.

From statement (2) we know that this concentration for the girls is the less than that for the the whole class, therefore, the one for the boys must be higher than that of the whole class, which must lie in the middle. – This statement on its on is Sufficient.

Weighted average is perhaps the most useful concept you can use on the GMAT. Even though you are more likely to use it on the Quant section, you may see it appear on a few verbal questions in Critical reasoning as well.

Remember that the “concentration” of the whole can never be more or less than that of any of the parts that make up the whole, and must lie in between.