Finance and Investments

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In a class of 200 students, 30 percent are enrolled in a finance course, and 40 percent are enrolled in an investments course. What percentage of the class is enrolled in neither a finance course nor an investments course?

(1) 25 percent of the class is enrolled in an investments course but not in a finance course.

(2) 15 percent of the class is enrolled in a finance course and also in an investments course.

Review: Finance and Investments




Explanation

This question looks ripe for the application of the Venn diagram formula for two groups, , which is covered in the Math Review of this course. As discussed in the Math Review, you can reassure yourself of the equation if necessary by drawing the overlapping Venn circles and re-deriving the formula. Putting in the values we know, we have , and we are asked for N, so we need B, the number of students enrolled in both finance and investments. On to the statements, evaluating them separately first.

Looking for "both," we skip to Statement (2). There it is. Statement (2) is sufficient.

Back to Statement (1). It's not what we were looking for, but we will analyze by cases before jumping to a conclusion. If 40% are in investments (from above), and 25% are in investments and not finance (per this statement), then the difference, which happens to be 15%, is enrolled in investments and finance. So we have obtained the value of "both" again. Statement (1) is sufficient.

The correct answer is (D).


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