Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 Apr 2015, 10:11

### 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 June
Open Detailed Calendar

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

Author Message
TAGS:
Manager
Joined: 07 Feb 2010
Posts: 160
Followers: 2

Kudos [?]: 171 [2] , given: 101

All of the students of Music High School are in the band [#permalink]  27 Nov 2010, 06:12
2
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

72% (03:24) correct 28% (02:30) wrong based on 185 sessions
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Nov 2012, 04:57, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 27123
Followers: 4187

Kudos [?]: 40494 [7] , given: 5540

Re: music high school [#permalink]  27 Nov 2010, 07:28
7
KUDOS
Expert's post
4
This post was
BOOKMARKED
anilnandyala 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

11

{total} = {band only} + {orchestra only} + {both};

As {band only} + {orchestra only} = 80% and {band only} = 50% then {orchestra only} = 30%.

So, {band}= 100% - {orchestra only} = 70% --> 70% of {total} = 119 --> {total} = 170 --> {orchestra only} = 30% of {total} = 51.

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5433
Location: Pune, India
Followers: 1325

Kudos [?]: 6720 [21] , given: 176

Re: music high school [#permalink]  27 Nov 2010, 12:55
21
KUDOS
Expert's post
Look at the diagram below:
If total 80% students are in one group, and 50% are in band only then 30% must be in orchestra only. Remaining 20% must be in both.
Total 70% students are in band and this number is equal to 119.
Attachment:

Ques2.jpg [ 13.21 KiB | Viewed 4339 times ]

70% of total students = 119 so total students = 170
No of students in orchestra only = 30% of 170 = 51
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29!

Veritas Prep Reviews

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2035
Followers: 135

Kudos [?]: 1100 [0], given: 376

Re: Sets [#permalink]  14 Mar 2011, 00:48
AnkitK wrote:
All of the students of music high school are in the band ,the orchestra or both.80 percent of students are in one group.There are 119 students in the bands.If the 50 percent of the students are in the band only,how many students are in the orchestra?

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

If 50% of the students are in the band only; then the group that contains 80% of the students must be the band group.

However, if I try to find 0.8x = 119; x is coming as a decimal, which is not possible.

Wonder, what am I doing wrong!!!
_________________
Manager
Joined: 11 Feb 2011
Posts: 141
Followers: 3

Kudos [?]: 56 [0], given: 21

Re: Sets [#permalink]  14 Mar 2011, 00:54
Dear Fluke ,even i am facing the same problem and not able to find the solution.lets see if anybody else has better technique.
_________________

target:-810 out of 800!

SVP
Joined: 16 Nov 2010
Posts: 1687
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 31

Kudos [?]: 340 [0], given: 36

Re: Sets [#permalink]  14 Mar 2011, 01:18
I also tried it like this, but getting a fraction :

Let a be the total # of students only in orchestra, b be the total # of students only in Band and Let x be the common # of students in Band and Orchestra

b +x = 119

b = 1/2(a + b +x)

2b = a + b + 119 - b => 2b = 119 + a

x = 30/100(a + b + x)

=> 119 - b = 3/10( a + 119)

119 - (119 + a)/2 = 3/10(a + 119)

119/2 - a/2 = 3a/10 + 119 * 3/10

119 ( 1/2 - 3/10) = a(1/2 + 3/10)

119 * 2/10 = a ( 8)/10)

=> a = 119 * 2/8
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Manager
Joined: 02 Apr 2010
Posts: 103
Followers: 5

Kudos [?]: 97 [0], given: 18

Re: music high school [#permalink]  14 Mar 2011, 03:28
My solution:

Let's define variables as follows:

w = # students in orchestra only
x = # students in band only
y = # students in both band & orchestra
z = # students who are neither in band nor orchestra
t = total # students

From question we know the following

All of the students of Music High School are in the band, the orchestra, or both
=> (i) z = 0

80 percent of the students are in only one group
=> (ii) 0.8*t = w + x

There are 119 students in the band
=> (iii) x + y = 119

If 50 percent of the students are in the band only
=> (iv) x = 0.5*t

From (i) and (iv) follows (v) w = 0.3*t

Given that (iv) x = 0.5*t and (v) w=0.3*t => y = 0.2*t

Since (iii) x + y = 119 => t = 170

Hence, w = 0.3*170 = 51
SVP
Joined: 16 Nov 2010
Posts: 1687
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 31

Kudos [?]: 340 [0], given: 36

Re: music high school [#permalink]  14 Mar 2011, 23:21
Ok, here is my retake, I couldn't figure this line earlier :

Let x be the total # of students.

B + C - B&C = x

Given that -> B - B&C = 0.5x

=> C = 0.5x

NOw, given that 80 percent of the students are in only one group => B - B&c + C - B&C = 0.8x
=> B&C = 0.2x and C - B&C = 0.3x

Also given that B = 119, so B + B&C = 0.7x = 119 => x = 170 and 0.3x = 51, so the answer is B.
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 662
Followers: 36

Kudos [?]: 348 [0], given: 39

Re: music high school [#permalink]  15 Mar 2011, 04:51
VeritasPrepKarishma wrote:
Look at the diagram below:
If total 80% students are in one group, and 50% are in band only then 30% must be in orchestra only. Remaining 20% must be in both.
Total 70% students are in band and this number is equal to 119.
Attachment:
Ques2.jpg

70% of total students = 119 so total students = 170
No of students in orchestra only = 30% of 170 = 51

How can i reason that "total 80% students are in one group" 30 percent for orchestra and 50%band. Why not 50 percent for band and 30% for both?
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5433
Location: Pune, India
Followers: 1325

Kudos [?]: 6720 [1] , given: 176

Re: music high school [#permalink]  15 Mar 2011, 08:01
1
KUDOS
Expert's post
Baten80 wrote:
VeritasPrepKarishma wrote:
Look at the diagram below:
If total 80% students are in one group, and 50% are in band only then 30% must be in orchestra only. Remaining 20% must be in both.
Total 70% students are in band and this number is equal to 119.
Attachment:
Ques2.jpg

70% of total students = 119 so total students = 170
No of students in orchestra only = 30% of 170 = 51

How can i reason that "total 80% students are in one group" 30 percent for orchestra and 50%band. Why not 50 percent for band and 30% for both?

Look at the question again:

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?

It says 80% students are in 1 group only (either orchestra only or band only but not both). The leftover 20% must be in both the groups, orchestra as well as band. (since every student is in at least one group)
Say, out of 100 students, 80 are in only one group. 50% students are in band only. So we now know how the 80% of 'one group only' is split: 50% in band only and 30% in orchestra only.
Look at the diagram in my previous post for more clarity.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29!

Veritas Prep Reviews

Intern
Joined: 01 Apr 2013
Posts: 23
Followers: 0

Kudos [?]: 18 [0], given: 9

Re: All of the students of Music High School are in the band [#permalink]  01 Apr 2013, 15:27
As it is an overlapping set problem, could someone show us how to solve this pb with the Double Matrix method ?

I find it hard to model the pb using this mthd

_________________

Intern
Joined: 09 Feb 2013
Posts: 7
Followers: 0

Kudos [?]: 2 [0], given: 6

Re: All of the students of Music High School are in the band [#permalink]  19 May 2013, 05:26
The official solution is below.

This is an overlapping sets problem concerning two groups (students in either band or orchestra) and the overlap between them (students in both band and orchestra).

If the problem gave information about the students only in terms of percents, then a smart number to use for the total number of students would be 100. However, this problem gives an actual number of students (“there are 119 students in the band”) in addition to the percentages given. Therefore, we cannot assume that the total number of students is 100.

Instead, first do the problem in terms of percents. There are three types of students: those in band, those in orchestra, and those in both. 80% of the students are in only one group. Thus, 20% of the students are in both groups. 50% of the students are in the band only. We can use those two figures to determine the percentage of students left over: 100% - 20% - 50% = 30% of the students are in the orchestra only.

Great - so 30% of the students are in the orchestra only. But although 30 is an answer choice, watch out! The question doesn't ask for the percentage of students in the orchestra only, it asks for the number of students in the orchestra only. We must figure out how many students are in Music High School altogether.

The question tells us that 119 students are in the band. We know that 70% of the students are in the band: 50% in band only, plus 20% in both band and orchestra. If we let x be the total number of students, then 119 students are 70% of x, or 119 = .7x. Therefore, x = 119 / .7 = 170 students total.

The number of students in the orchestra only is 30% of 170, or .3 × 170 = 51.

I'm in confusion in the below sentence. Can someone please elaborate?

"We know that 70% of the students are in the band: 50% in band only, plus 20% in both band and orchestra"
Intern
Joined: 05 Mar 2013
Posts: 45
Location: India
Concentration: Entrepreneurship, Marketing
GMAT Date: 06-05-2013
GPA: 3.2
Followers: 1

Kudos [?]: 25 [2] , given: 14

Re: All of the students of Music High School are in the band [#permalink]  19 May 2013, 05:49
2
KUDOS
connexion 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?

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

Attachment:

Untitled4.jpg [ 16.74 KiB | Viewed 2573 times ]

Let the total number of students be x

119 = only band + both

0.8x = only band + only orchestra

which also implies 0.2x students are in both(x-0.8x)

0.5x = only band

which implies only orchestra = 0.3x

So number of students in band = 0.5x + 0.2x = 0.7x = 119 which gives x as 170

So the number of students in orchestra only is 0.3*170 = 51

_________________

"Kudos" will help me a lot!!!!!!Please donate some!!!

Completed
Official Quant Review
OG - Quant

In Progress
Official Verbal Review
OG 13th ed
MGMAT IR
AWA Structure

Yet to do
100 700+ SC questions
MR Verbal
MR Quant

Verbal is a ghost. Cant find head and tail of it.

Senior Manager
Joined: 28 Apr 2012
Posts: 308
Location: India
Concentration: Technology, General Management
GMAT 1: 650 Q48 V31
GMAT 2: 770 Q50 V47
WE: Information Technology (Computer Software)
Followers: 17

Kudos [?]: 242 [0], given: 142

Re: All of the students of Music High School are in the band [#permalink]  19 May 2013, 07:23
connexion 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?

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

80% Students are only in one group. => 20% are in both group
50% students are in band only =>

i. 50% (Band Only)+ 20%(both Band and Orchetsra) = 70% are in the band = 119 Students(given)
ii. 80% (Either only in Band or Only in Orchestra) - 50%(only in Band) = 30% are in only Orchestra

If $$70% = 119 => 30% = 119*(30/70) = 51$$(Ans = B)
_________________

"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well."
― Voltaire

Press Kudos, if I have helped.
Thanks!

shit-happens-my-journey-to-172475.html#p1372807

Manager
Joined: 25 Oct 2013
Posts: 173
Followers: 0

Kudos [?]: 30 [0], given: 56

Re: All of the students of Music High School are in the band [#permalink]  25 Jan 2014, 02:26
Initially it was difficult for me to understand the question. But solved in 3 mins.

Let t be total number of students.

80% is in only one group => 0.8t
50% is in only band => 0.5t so 0.8t-0.5t = 0.3t is in Only Orchestra.

Now,
Orchestra Only + both + Band Only = t
0.3t + x + 0.5t = t

It is given that 119 are in band means 0.5t+x = 119
So,
0.3t+119 = t
t = 119/0.7 = 170

Orchestra Only = 0.3t = 0.3*170 = 51 ---B is the answer.
_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Intern
Joined: 18 Jan 2015
Posts: 6
Location: United States (MN)
Concentration: General Management, Entrepreneurship
Schools: Carlson
GMAT Date: 04-27-2015
GPA: 3.76
WE: Engineering (Manufacturing)
Followers: 0

Kudos [?]: 6 [0], given: 1

Overlapping of Sets [#permalink]  23 Jan 2015, 09:19
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
_________________

Two Years at Harvard Business School

Math Expert
Joined: 02 Sep 2009
Posts: 27123
Followers: 4187

Kudos [?]: 40494 [0], given: 5540

Re: All of the students of Music High School are in the band [#permalink]  23 Jan 2015, 10:15
Expert's post
kler515 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?

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

Merging similar topics. Please refer to the solutions above.

_________________
Re: All of the students of Music High School are in the band   [#permalink] 23 Jan 2015, 10:15
Similar topics Replies Last post
Similar
Topics:
4 At a certain school, 100 students are in the marching band. If 40% of 4 10 Nov 2014, 08:04
1 290 students at Music High School are in the band, the 3 07 May 2013, 01:14
2 If 90 students auditioned for the school musical, how many 3 26 Aug 2012, 02:16
4 All of the students of Music High School are in the band, 8 24 Aug 2008, 21:15
All students at Lincoln High School study at least one of 13 14 Jun 2005, 00:59
Display posts from previous: Sort by