Data Sufficiency

We want to know how many of the 250 students mentioned in the stem are in student government but not in debate (everyone is in at least one of the two groups, so if someone is not in debate, he or she must be in government only).

Using Statement 1, we know 80 are not in government, so the rest, or 250 - 80 = 170, must be in government. The stem tells us that 40 of these people are also in debate, so the rest, or 170 - 40 = 130, are not in debate.

I'd use a Venn diagram, but that's a bit hard to draw here!

If you were trying to use a formula here when only looking at Statement 1, notice that the 250 in the question does not include the 'neither' group. So 250 is only equal to the "only A + only B + both" part of your formula (and the minus sign in your formula in front of "Both" needs to be a plus sign). When you use Statement 2, you discover that Neither = 150, and the Total is therefore 400 (not 250), but we don't need that information to answer the question.

I thought I'd point out that iwgi's approach (known as the Double Matrix Method) 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:
- participates in debate or doesn't participate in debate
- participates in student government or doesn't participate in student government

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, 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/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.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