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

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

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.

I don't understand- with some questions we have to assume there could be a third set but for some it's only what's mentioned?! Have I missed it being hinted implicitly?
Also, it mentions total of Arts and Science. Is it the intersection or the Total. Don't we hint the total with ORs?

Bunuel