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?

Venn Diagram is still the best way to go about it.
80 % are only in Band (B) or Orchestra (O)
50 % is only in B so 30 % will be only in O.
Remaining 20% in intersection of B and O or the students who are in both O and B.
so 70% = 119
30 % = (119/7) * 30

IMO B

girish3131 wrote: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?


30
51
60
85
119


i knw it's already thr but still cudn't get crux of it.. so posting ....

let band only=x
bth=y
and orchestra=z
tot=n
80 percent of the students are in only one group.------->x+z=0.8n

There are 119 students in the band.----->x+y=119

50 percent of the students are in the band only------>x=0.5n----->y+z=0.5n

how many students are in the orchestra only---->z=???

now x=0.5n---->z=0.3n
x+y=119----->y=119-0.5n
putting value of y and z in y+z=0.5n---->119-0.5n+0.3n=0.5n solving n=170
and z=0.3n---->z=51

Thanks 4 yr response Guys...

it wud be great if u can show yr data in venn diagram...

am still struggling to make venn diagram with given data....

as i understood that band ONLY -> 50 %

then orchestra ONLY must be 80 % because this is the only remaining froup.... ???

girish3131 wrote:Thanks 4 yr response Guys...

it wud be great if u can show yr data in venn diagram...

am still struggling to make venn diagram with given data....

as i understood that band ONLY -> 50 %

then orchestra ONLY must be 80 % because this is the only remaining froup.... ???

hey i have tried my level best to make a venn dia hope it helps

WOW thepheonix..nice explanation.
Definitely appreciated.

This is an MGMAT question.

To me the phrasing "80% are in only one group" sounded wrong.This is a problem with most of the MGMAT questions where it just tires to make things difficult with hanging sentences!.

And i don't how it is again presumed that 80% is distributed into= '50% are in band and 30% are in orchestra' where its says in the beginning that 80% are in only one group!

Aslan you very right.This question can still be solved though.If you know,there is Gold credit card and platinum credit card (balance ) question.The meaning of balance in that question is totally different from the conventional -leftover ,and as a result,the question has stumped many a people.

This can also be said for some CR and RC questions in which the answers totally seem far fetched.

The correct answer to this question is indeed 51.I can't solve this question because I'm exhausted after taking the Manhattan CAT.

I got this question right.

Is it just me or other too feel that MGMAT quant has gotten easier.The last time I took the CAT I got a 51 on quant.Since I took in untimed mode,I took it for an exception.This time I timed the test and still comfortably got a 51.I never felt rushed during the test.

I hope that I repeat this on the real deal.

@rishab1988:Good luck to you buddy...51Q on MGMAT is some feat!