Another popular GMAT word problem involves the overlapping set. While the official GMAT book recommends solving these problems with a Venn diagram, a best practice approach is to use a table to organize your information.

### Example

10% of the students in the graduating class study French but not Japanese. 50% of the students who study Japanese also study French. If 40% of the students in the graduating class study French, what percentage of students in the graduating class study Japanese?

1. 20%
2. 30%
3. 40%
4. 50%
5. 60%

### Solution

1. The question is asking how many students study Japanese.
2. Since we are only trying to solve for one variable, let x = # students that study Japanese
3. In a 2 set overlapping set problem, organize the information into a table. Since this problem is providing information in percents, we can pick 100 as the total. This will come in make it easier to perform calculations later. Pay special attention to the wording of the problem. Notice in the second sentence that the problem does not tell us that 50% of the students study French, but 50% of the students that study Japanese study French. There is a clear distinction because we have x as the total number of students studying Japanese; students studying both French and Japanese is equal to 0.5x.

4. Setup a mathematical relationship. Using our chart it’s easy to see that we can tally up the French column to solve for x.
5. Solve

60% of the students study Japanese. The answer is E.