GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 11 Dec 2018, 10:07

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
• ### The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# All of the students of Music High School are in the band,

Author Message
Intern
Joined: 19 Jul 2008
Posts: 23
All of the students of Music High School are in the band,  [#permalink]

### Show Tags

Updated on: 11 Nov 2012, 05:01
2
9
00:00

Difficulty:

55% (hard)

Question Stats:

71% (01:12) correct 29% (01:05) wrong based on 395 sessions

### HideShow timer Statistics

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. 11

OPEN DISCUSSION OF THIS QUESTION IS HERE: all-of-the-students-of-music-high-school-are-in-the-band-105432.html

Originally posted by gmatcraze on 24 Aug 2008, 21:15.
Last edited by Bunuel on 11 Nov 2012, 05:01, edited 2 times in total.
Renamed the topic, edited the question and moved to PS forum.
SVP
Joined: 29 Aug 2007
Posts: 2366
Re: Music High School - set theory  [#permalink]

### Show Tags

24 Aug 2008, 21:54
gmatcraze 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

not sure i got it...how the number in a group can be with 80% or 50% or 30% or 20%?

band = b
orchestra = o
band & orchestra = oc
total = b+o - oc

if 50% are only in the band then total in band = 80%
oc = 30%
c = 20%

so 80% of total = 119
total = 140
c = 31 or 30
A.
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Intern
Joined: 03 Mar 2008
Posts: 43
Re: Music High School - set theory  [#permalink]

### Show Tags

24 Aug 2008, 22:27
8
4
gmatcraze 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

B = Band
O = Orchestra
T = Total

Only Band = 0.5T
Either Band or Orchestra but not both = 0.8T
Hence, Only Orchestra = 0.3T
Also, both is 1 - 0.8T = 0.2T

0.5T + 0.2T = 119
T = 170

Hence, Only Orchestra = 0.3T = 51
Director
Joined: 23 May 2008
Posts: 696
Re: Music High School - set theory  [#permalink]

### Show Tags

25 Aug 2008, 09:41
D

let T= total
let X= orchestra only
80% in only one group means 20% or .2T in both groups

119 - .2T = .5T
119= .7T
T=170

119 + X - .2T =170

.2T=34 (.2*170)

119 + X -34 = 170

X=85
Manager
Joined: 05 Feb 2007
Posts: 135
Re: Music High School - set theory  [#permalink]

### Show Tags

07 Mar 2009, 16:29
I use a table for set theory with 2 sets.

Orch no-Orch Total
---------------------------------------
Band .2(x) .5(x) 119
No-Band ? 0
Total .5(x) .5(x) x

From this we can conclude

.2(x) + .5(x) = 119
.7(x) = 119
x = 170

fill in the rest and we get .5(x) - ? = .2(x)
which is 85-34 = 51

51

what is the OA?
Current Student
Joined: 03 Aug 2006
Posts: 110
Re: Music High School - set theory  [#permalink]

### Show Tags

07 Mar 2009, 22:44
2
1
1
For me the answer is 51.

Given: % of students in one group only = 80% ---- 1.
Therefore % of students in both groups = 100 - 80 = 20% -----2.
Also given: % of students in the band only = 50% -----3.
Also given: Number of students who are in band = 119 -----4.

From 2, 3, and 4.

50% + 20% = 70% = 119 Students

Finding total students:

If 70 out of 100 then 119 out of x
Solving for x

x = (119 x 100)/70
x = 170

Students in orchestra only = 170 - 119 = 51
Director
Joined: 25 Oct 2006
Posts: 551
Re: Music High School - set theory  [#permalink]

### Show Tags

09 Mar 2009, 17:47
I also got 51 (B)

Band = 50% of Students and Orchestra = 30% of students [both group consists of 80% of students]
Now students who are both in two groups are 20% of students.

So total Band:
50% of Students + 20% of students = 119
Students = 170.

Hence only orchestra = 30% of students = 30% of 170 = 51
_________________

If You're Not Living On The Edge, You're Taking Up Too Much Space

Intern
Joined: 10 May 2009
Posts: 16
Location: United States
Concentration: Entrepreneurship, Organizational Behavior
Schools: Cranfield '16
GMAT Date: 11-25-2012
GPA: 2.67
Re: All of the students of Music High School are in the band,  [#permalink]

### Show Tags

09 Nov 2012, 09:38
What level of question is this?
Math Expert
Joined: 02 Sep 2009
Posts: 51100
Re: All of the students of Music High School are in the band,  [#permalink]

### Show Tags

11 Nov 2012, 05:00
1
magicmanisha wrote:
What level of question is this?

Difficulty level is ~650.

OPEN DISCUSSION OF THIS QUESTION IS HERE: all-of-the-students-of-music-high-school-are-in-the-band-105432.html
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 9115
Re: All of the students of Music High School are in the band,  [#permalink]

### Show Tags

13 Aug 2018, 22:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: All of the students of Music High School are in the band, &nbs [#permalink] 13 Aug 2018, 22:13
Display posts from previous: Sort by