At a graduation ceremony, some students earned bachelors in science de

Question

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.

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

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

peachfuzz · Answer

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 studentd who have BA degrees but we dont knoe the breakdown of students with BS degrees.
insufficient

Answer : A

aimtoteach · Answer

Total student  – 200

Statement A   – 120 did only a bachelor in arts. This implies that the remaining (200-120=80) did a bachelor in sciences. This means the part of the overlapping set that covers Sciences and Both.

Sufficient

Statement B:   With the information that 40 students graduated only in science, we have 2 unknowns – how many graduated both and how many graduated only science.

Insufficient.

Hence A is the correct answer

Thanks,
aimtoteach

**Please give Kudos if the explanation was helpful**

imsahlahno · Answer

total no. of students given are 200.

Let the no. of students with bachelor's in only science be S, in only arts be A and in both be B.

a) Given that A = 120.
Now 200 = S + A + B
thus S + B = 200 - A = 200 -120 = 80.
Thus total students with bachelor's in science = 80. Sufficient

b) Given that S = 40.
Thus A + B = 160. And we cannot calculate A or B individually to calculate total no. of students with bachelor's in science. Insufficient.

Thus ans is A

Bunuel · Answer

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.

pierjoejoe · Answer

i fumbled this question for a dummy reason. The question clearly states that there are in total 200 students who "received bachelors degrees in the arts and sciences". i interpreted it as students who earned a degree in BOTH arts and science.

is there any kind of wordings that we can use to avoid this error?

is there any kind of wordings that we can use to avoid this error?

Bunuel · Answer

I see your point, and the wording could probably have been clearer. However, if the highlighted part meant what you thought, it would probably be phrased as something like "200 students received bachelors degrees in BOTH the arts and sciences."

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At a graduation ceremony, some students earned bachelors in science de

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