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10 Nov 2014, 09:04
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
82% (01:49) correct
18%
(01:48)
wrong
based on 409
sessions
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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.
10 Nov 2014, 11:31
Kudos
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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.
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.
10 Nov 2014, 20:02
Kudos
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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
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
