At a graduation ceremony, some students earned bachelors in

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Veritas Prep

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.

OA A

[Jay@ManhattanReview]

Veritas Prep

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.

OA A

Say,

# of students who earned degrees in Art and Science = T = 200;
# of students who earned degree ONLY in Science = S;
# of students who earned degree ONLY in Arts = A;
# of students who earned degree in both Art and Science = B

=> # of students who earned degree in Science = S + B

Thus, T = S + B + A

200 = S + B + A

We have to get the value of S + B.

Let's take each statement one by one.

1) 120 students earned only a bachelors in arts.

=> A = 120

Thus, 200 = S + B + A => 200 = S + B + 120 => S + B = 80. Sufficient.

2) 40 students earned only a bachelors in science.

=> S = 40. Can't get the value of B. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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