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At a graduation ceremony, some students earned bachelors in

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At a graduation ceremony, some students earned bachelors in

by AAPL » Sat Mar 16, 2019 6:21 am

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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
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Mar 18, 2019 12:28 am

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AAPL wrote: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,

The number of students who earned bachelors degree only in science = s;
The number of students who earned bachelors degree only in arts a;
The number of students who earned bachelors degree only in science and art both = b

Thus, we have s + b + a = 200.

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, s + b = 200 - 120 = 80. Sufficient.

2) 40 students earned only a bachelors in science.

=> s = 40. Since we do not know the value of b or a, we can't get the value of s + b. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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by swerve » Mon Mar 18, 2019 9:11 am

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200 total students

(1) 120 students earned only a bachelors in arts.
120 with BA degrees
200-120 = 80 BS degrees
Sufficient

(2) 40 students earned only a bachelors in science.
40 non BA students with BS degrees. We know there are 160 students who have BA degrees but we don't know the breakdown of students with BS degrees.
Insufficient

Therefore, __A__
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