Graduation Ceremony

[manik11]

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.

Experts..can you show me how to solve this one using the double matrix method?

OA : A
Source : Veritas Prep

[Matt@VeritasPrep]

It might be easier to avoid the matrix method for S1. We know that Arts + Sciences = 200. We're told that Arts-Only = 120. So the remaining 80 must be Science (we don't care how many of those 80 are Science-Only, since we only want to know about Science in any capacity), and S1 is sufficient.

For S2, we have the opposite result: 40 ONLY in Science, so 160 in either Arts-Only or Arts+Science. But we can't distinguish Arts-Only from Arts+Science here, so S2 is NOT sufficient.

This is also a great problem on which to AVOID C. C is just way too easy - too good to be true!

[DavidG@VeritasPrep]

Matt's right that we don't necessarily need the matrix here. But if you love matrices (and who doesn't?) here's how it would look:

To start, we know that there 200 students receiving arts or science degrees. So we know that no one within this population is receiving neither an art or a science degree. And we're looking for the total science degrees. Our starting matrix will look like this:




Statement 1 tells us that 120 students earned only an arts degree. So art/not science = 120. If we fill in everything we can, we end up with the following:




Total science = 80, so sufficient.

Statement 2 tells us that 40 students earned only a science degree. Filling in our matrix, we get the following:




No way to determine the total who earn science degrees, so statement 2 is not sufficient. So our answer is A.