At a certain school, 100 students are in the marching band. If 40% of

Question

Tough and Tricky questions: Overlapping Sets.

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.

Kudos for a correct  solution .

DangerPenguin · Answer

Here was my work in about 1min30sec, I chose answer C.

Here is the relevant info we have and the info we need:
# of students in orchestra: - if we find out this #, we know the # in both since 40% of this # will equal the # of students in both
# of students in marching band: 100 - given
# of students in both: if we find out this #, we know the # for orchestra
# of students not in orch/march.: ???? This is the answer we need
Total # of students: ??? - not given

statement 1: not sufficient
We find out how many students there are total which is good but we still don't know the # of students in orchestra or the # of students in both.

statement 2: not sufficient
We find out how many students are in orchestra which tells us the # of students in both. However, we don't know the total # of students so we still don't know how many students are in neither.

Both statements together will give us all of the information we need to find out how many students are in neither. Answer C.

kinghyts · Answer

Let M represent marching band, O orchestra, B both and N for none

Total no of students = M + O - B + N

From Statement 1, which gives us the total number of students = 1000

We know M = 100, therefore
 1000 = 100 + O - B + N

We cannot determine N and therefore insufficient

From Statement 2, we know that 50 students are in orchestra but don't know the total number of students. Hence insufficient.

Combining 1 and 2, we can say

1000 = 100 + 50 - B+ N

B = 40/100 * 50 = 20

Therefore, N = 1000 -130 = 870. Sufficient.

Therefore C) should be the answer

killgmatagain · Answer

Here's my cooking formula, skipping all term formalities & rework, I have a...

Total = Orchestra + Marching Band - Overlap + Both Neither (O & M.Bd)

Ingredients;
O.L. = 20 (40% of Orc.)
Orc. = 50 (100%) - 20 (40%)
M.Bd = 100 - 20

(Total = 1000 Stu.)

Mixed the salad and you get;

Neither = Total - Orc. + M.Bd - Overlap = >
1000 - 20 - 30 - 80 = 870

Therefore C

Yummy,
JADS

santorasantu · Answer

C

From stem: n(M) = 100, if n(O) = x, then n(MnO) = 0.4x

from 1: n(MuO) = n(M) + n(O) - n(MnO) + neither
1000 = 100 + x -0.4x +neither
no info on x, NSF

from 2: x= 50, we do not know the value of n(MuO), so NSF

1+2 :
1000 = 100 + 50 - 0.4*50 + neither
we can find, the value as there is only 1 unknown 
sufficient.

Please provide OA, Bunuel.

bumpbot · Answer

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At a certain school, 100 students are in the marching band. If 40% of

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