overlapping sets DS question from MGMAT CAT

[raja_asu]

At a certain school, 100 students are in the marching band. If 40% of the students in the orchestra are also in the marching band, how many students are members of neither the orchestra nor the marching band?

(1) There are 1000 students in the school.

(2) 50 students are in the orchestra.

The answer is C. But, I chose E.

My explanation is , never in the question mentioned that all the students in the school are in either orchestra or marching band. So, (1) is an useless data.
Can u please tell me how to respond to these type of questions in the real GMAT test?

Thanks,

Rajesh

[StaceyKoprince]

The question doesn't mention that all of the students in the school are in either orchestra or marching band because that's not a true statement for this problem. In fact, the question ("how many students are members of neither the orchestra nor the marching band?") implies that there are some students who do not participate in either activity.

Statement 1 is not useless - 1 is necessary, combined with 2, to solve the problem.

Given:
100 students in marching band
40% of orchestra students are in marching band

how many students are in neither?

There are 4 possibilities:
A) students in orchestra
B) students in marching band
C) students in orchestra AND marching band
D) students in NEITHER orchestra OR marching band

Formula for these "both / neither" problems is:
Total = Group1 + Group2 - Both + Neither
Total = 100 + Group2 - Both + Neither (since I know there are 100 in marching band)

(1) 1000 total students. 1000 = 100 + Group2 - Both + Neither. Insuff. Elim A and D
(2) 50 students in orchestra. So 20 of those are also in marching band. Total = 100 + 50 - 20 + Neither. Insuff. Elim B.
(1) + (2). 1000 = 100 + 50 - 20 + Neither. I can solve for Neither. Suff. Answer is C.