Music high School

[love_with_uuuu]

All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?

A) 30
B) 51
C) 60
D) 85
E) 119

I was not able to understand the explanation :(

[love_with_uuuu]

I got it.. Moderators please delete the thread..

[cfaking]

very good Q.
hats off to MGMAT team

Band only + both + orchestra only = total students

soln:
band only =50%

also band only + orchestra only = 80%
hence, orchestra only =30%


Now, 70%(Total)=119===>total=170===>orchestra (only) =51

[RonPurewal]

looks like everything is good with this thread.

peace

[bonsfi]

Another way to solve using plugIN!
Answers give the values for orchestra only:
30
51
60
85
119

Because we know that the band has 119 students, we have the total # of students (band + orchestra only = total):
30 + 119 = 149
51 + 119 = 170
60 + 119 = 179
85 + 119 = 204
119 + 119 = 238

Because 50% of total is band only, we can check the results:
149/2 = not halve person!
170/2 = 85
179/2 = not halve person!
204/2 = 102
238/2 = 119
A and C are OUT!

Because 80% total are only one group, 20% total are for both:
149 OUT!
170/2 = 85
179/2 OUT!
204*0,2 is not an integer
238*0,2 is not an integer
D and E are OUT!

ONLY B works with integers!

[Ahmed_elghaflol]

thanks for the q

i have another solution which i think more simple:

imagine that this is a schedule

___________orchestra______not orchestra______total
.
Band__________20%___________50%_____________70%
.
Not band______30%_____________0%____________30%
.
Total_________50%____________50%___________100%
..
..
the numbers in bold is from the question
20% ==> 100% - 80%
30% ==> 80% - 50%
..
so the question if 70% =119 student , how many is 30%?
the answer is 51 students
..
..
..
This technique in answer of sets is from Manhattan GMAT Prep

[tim]

Thanks for all of your input..

[kiranck007]

Hi, I understand the explanation provided here, but I see a discrepancy in the question, and the way the problem is solved. What I understand by the statement "80 percent of the students are in only one group" is that 80% percent are in only a group i.e in either band group only or in orchestra group only; isn't that is what is supposed to be conveyed by the given statement? Please correct me, I am having difficulty in understanding sentence here. What it means to have

80% are in only one of the groups
80% are in one of the two groups
80% of the students are in only one group

[RonPurewal]

Hi, I understand the explanation provided here, but I see a discrepancy in the question

in this problem, that's a non-issue, because only one possible interpretation is consistent with the other statement in the problem ("50 percent of the students are in the band only").

if you interpret the first statement as "there's one group that, by itself, contains 80% of the students exclusively", then that contradicts this second statement. so, oops, i guess it's the other interpretation.

also, that's just the way this sort of statement is written in the english language. i see your point, but, can you come up with a less ambiguous way of writing that statement? probably not.