Data Sufficiency

Mitch, it looks like you've accidentally posted the solution to the wrong problem here.

There are two easy ways to solve an OVERLAPPING SETS problem like this: a matrix or a Venn diagram

MATRIX:
Students can either take French or not, and they can take Spanish or not. Set up your categories like this:



Then, fill in the given information, and make inferences:



It's important to note here that students can only take French, Spanish, or both - no one is taking NEITHER. We can put a 0 in the "no French, no Spanish" box, and extrapolate from there:



Now, fill in the information from the statements. If 60 do not study Spanish, we can add that to the "no Spanish" total, but we can also add it to the "French but no Spanish" box. We can infer from there that 140 students take both. Sufficient:



The second statement allows us to fill in that 240 student take Spanish, from which we can infer that 60 do not study Spanish... the same thing that statement 1 told us. This is also sufficient.

The answer is D.

VENN DIAGRAM:

Because in this problem, students can take only French, Spanish, or both - but not neither - a Venn diagram would also work well.

We have 300 total students. If 100 do not take French, they must take only Spanish:



In order to find how many students take both, we need to find the number that take French only, or total for Spanish.

Statement 1:
If 60 do not study Spanish, they must take French only. That means that the "both" section must be 140, because 60 + 140 + 100 = 300



Statement 2:
If 240 study Spanish, then 140 must study both, because 140 + 100 = 240




Both statements are sufficient.

For more on OVERLAPPING SETS, see:
https://www.beatthegmat.com/rainbow-trou ... tml#555603
https://www.beatthegmat.com/ds-question- ... tml#677080
https://www.beatthegmat.com/survery-resu ... tml#576105

ceilidh.erickson has done a great job demonstrating the Double Matrix Method.

This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- studying French or not studying French
- studying Spanish or not studying Spanish

If anyone is interested in learning this technique, we have a free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with the Double Matrix Method, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html

Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent