IMO its C

what is the OA?

Make a venn diagram with three circles. C M AND L.

C- On campus
M- more than 20
L- less than 20

Now erase the part of circle where C exists on its own, ie is not common to either M or L..since a student has to be either over 20 or 20 and less!

640 includes the entire circle M, 20 from statement 2 includes the part of circle L that is not common. we need to find the remaining portion that is common to circle C and circle L. total equals 800.....so we need both the statements


Hope you can put my explanation to paper and pencil and try it out.

I also go with C

what is OA?

# of 20 years less = 840 - 640 (20>= years old)

if you substract 60 from it, it gives # of <20 lives in campus.

Let group1 be "live on campus" and group2 be "is more than 20yrs old". We know that 250 ppl below to both groups. Because this is an overlapping groups question, we can use the overlapping group formula: Total= group1 + group2 + neither - both.

fill in what we know: 800= group1 + group2 + neither - 250

We want to know how many belong to group1 only. This is group1-both. Since we already know both, our rephrase is: "What is group1?"

Here is how the statements work together:
(1) group2=640.
(2) neither=60

By putting both of these in the group formula we get 800 = group1 + 640 + 60 - 250. This is enough to find group1 and answer the rephrase. The answer is C

An alternative detailed explanation and video solution can be found at GMATPrep question 1551.

Lordspace, if you have trouble with this type of question, you can use the Drill Engine to generate timed drills with similar questions. Set topic='Sets & Groups' and difficult='700+'

Good luck,
-Patrick

Lets try doing this by the grid method:

OnC = onCampus
OfC = offCampus

>20 = greater than 20 yrs
<20 = less than 20 yrs

basic grid :
------- | Onc | OfC
>20 |250 |
<20 | X |
Total | X | 800

we need to find X

Statement 1:
total students over 20 = 640
grid becomes:

------- | Onc | OfC |total
>20 |250 | 390| 640
<20 | X | ? | 160
Total | X | |800

cannot solve it even after filling the grid "?" needs to be answered


Statement 2: 60 students are <= 20 and live off campus

grid becomes:

------- | Onc | OfC |total
>20 |250 | ? | ?
<20 | X | 60 |
Total | X | |800

The grid has some missing information

with st1 and st2 combined
grid becomes:

------- | Onc | OfC |total
>20 |250 | 390| 640
<20 | X | 60 | 160
Total | 350 | 450 |800

(hence C)