Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 29 May 2017, 00:27

### 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

# The 39 parents participating in the Smithville PTA have been

Author Message
TAGS:

### Hide Tags

Intern
Joined: 24 Jan 2012
Posts: 9
Followers: 0

Kudos [?]: 151 [0], given: 3

The 39 parents participating in the Smithville PTA have been [#permalink]

### Show Tags

27 Sep 2013, 07:33
2
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

66% (02:45) correct 34% (01:58) wrong based on 157 sessions

### HideShow timer Statistics

The 39 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?

A. 4
B. 6
C. 8
D. 9
E. 10
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Sep 2013, 08:31, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 39042
Followers: 7751

Kudos [?]: 106499 [1] , given: 11626

Re: The 39 parents participating in the Smithville PTA [#permalink]

### Show Tags

27 Sep 2013, 08:30
1
KUDOS
Expert's post
6
This post was
BOOKMARKED
violetsplash wrote:
The 39 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?

A. 4
B. 6
C. 8
D. 9
E. 10

$$Total = A + B + C - (sum \ of \ EXACTLY \ 2-group \ overlaps) - 2*(all \ three) + Neither$$.

Since each parent is assigned to at least 1 of 3 committees, then the # of parents assigned to neither of them is 0.

$$39=21+18+19-x-2*5+0$$ --> $$x=9$$.

_________________
Intern
Joined: 06 Feb 2013
Posts: 23
Followers: 0

Kudos [?]: 4 [0], given: 3

Re: The 39 parents participating in the Smithville PTA have been [#permalink]

### Show Tags

27 Sep 2013, 11:09
The formula is Total = A+B+C - sum of exactly two + 2*all three + neither
21+18+19-x-2*5=39
solving for x you get 9
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15503
Followers: 651

Kudos [?]: 210 [0], given: 0

Re: The 39 parents participating in the Smithville PTA have been [#permalink]

### Show Tags

29 Aug 2015, 01:11
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.
_________________
Intern
Joined: 04 Sep 2015
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 14

Re: The 39 parents participating in the Smithville PTA have been [#permalink]

### Show Tags

27 Oct 2015, 07:15
1
This post was
BOOKMARKED
Could someone explain to me why it is necessary to double the amount of parents in all groups?

Thanks
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7380
Location: Pune, India
Followers: 2292

Kudos [?]: 15150 [1] , given: 224

The 39 parents participating in the Smithville PTA have been [#permalink]

### Show Tags

29 Oct 2015, 23:43
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
Condon wrote:
Could someone explain to me why it is necessary to double the amount of parents in all groups?

Thanks

This post tells you how you get the formula for n(Exactly two sets) and others:
http://www.veritasprep.com/blog/2015/10 ... ping-sets/

This is our standard formula:
Total = n(A) + n(B) + n(C) – n(A and B) – n(B and C) – n(C and A) + n(A and B and C) + n(No Set)
39 = 21 + 18 + 19 - (n(A and B) + n(B and C) + n(C and A)) + 5 + 0
(n(A and B) + n(B and C) + n(C and A)) = 24

Now let’s see how we can calculate the number of people in exactly two sets.
n(A and B) includes people who are in both A and B and it also includes people who are in A, B and C. Because of this, we should remove n(A and B and C) from n(A and B) to get n(A and B only). Similarly, you get n(B and C only) and n(C and A only), so adding all these three will give us number of people in exactly 2 sets.
n(Exactly two sets) = n(A and B) – n(A and B and C) + n(B and C) – n(A and B and C) + n(C and A) – n(A and B and C).

Therefore:
n(Exactly two sets) = n(A and B) + n(B and C) + n(C and A) – 3*n(A and B and C)
n(Exactly two sets) = 24 - 3*5 = 9

In other words, you can substitute from formula 2 into formula 1 to get
n(A and B) + n(B and C) + n(C and A) = n(Exactly two sets) + 3*n(A and B and C)

Put in formula 1:
Total = n(A) + n(B) + n(C) – (n(Exactly two sets) + 3*n(A and B and C)) + n(A and B and C) + n(No Set)
Total = n(A) + n(B) + n(C) – n(Exactly two sets) - 2*n(A and B and C)) + n(No Set)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15503
Followers: 651

Kudos [?]: 210 [0], given: 0

Re: The 39 parents participating in the Smithville PTA have been [#permalink]

### Show Tags

24 Mar 2017, 10:34
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.
_________________
Manager
Joined: 12 Mar 2013
Posts: 239
Followers: 8

Kudos [?]: 114 [0], given: 349

Re: The 39 parents participating in the Smithville PTA have been [#permalink]

### Show Tags

24 Mar 2017, 10:59
A+B+C - sum of exactly two - 2*all three
ans: D
_________________

We Shall Overcome... One day...

Re: The 39 parents participating in the Smithville PTA have been   [#permalink] 24 Mar 2017, 10:59
Similar topics Replies Last post
Similar
Topics:
15 A and B are two laborers who have been given the t 7 15 May 2017, 19:20
11 Sides of box have areas of 91, 39, 21. What is the volume? 7 07 May 2017, 16:07
16 In a family with 3 children, the parents have agreed to brin 15 27 Nov 2016, 12:23
3 Of the 800 employees of Company X, 70 percent have been with 5 01 May 2015, 02:42
7 Of the 800 employees of company X, 70% have been with the 7 23 Jul 2015, 02:04
Display posts from previous: Sort by