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?

- 20%
- 30%
- 40%
- 50%
- 60%

### Solution

- The question is asking how many students study Japanese.
- Since we are only trying to solve for one variable, let x = # students that study Japanese
- Setup a mathematical relationship. Using our chart it’s easy to see that we can tally up the French column to solve for x.
- Solve

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.

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

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