Bunuel wrote:

At a graduation ceremony, some students earned bachelors in science degrees, some earned bachelors in arts degrees, and some students double-majored and earned both degrees. If 200 students in total received bachelors degrees in the arts and sciences, how many students earned bachelors in science degrees?

(1) 120 students earned only a bachelors in arts.

(2) 40 students earned only a bachelors in science.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:A. In this Venn Diagram problem, it is important to recognize that there is no "neither" group - all 200 people earned at least one degree so you don't need to worry about anyone who did not earn one. Accordingly, your equations set up as either:

Arts + Sciences - Both = 200

or

Arts Only + Sciences Only + Both = 200

Statement 1 gives you the number of Arts Only as 120, meaning that you can use the second equation to see that:

120 + Sciences Only + Both = 200

Then you need to recognize that the question asks specifically for how many people received science degrees, total. In this way, if you received only a science degree OR if you received both an arts and a science degree, you count toward "Science Total", so you know that the remaining 80 people who did not receive only an arts degree must have received a science degree. Statement 1 is thus sufficient.

Statement 2 is not sufficient, as it only tells you about the "only science" group and not the "both" group, and both "science only" and "both science and arts" count toward the science total that you need.

The correct answer is A.

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