A committee consists of n women and k men. In addition there : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 07:37

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

A committee consists of n women and k men. In addition there

Author Message
TAGS:

Hide Tags

Intern
Joined: 13 Feb 2012
Posts: 20
WE: Other (Transportation)
Followers: 0

Kudos [?]: 39 [4] , given: 14

A committee consists of n women and k men. In addition there [#permalink]

Show Tags

15 Feb 2012, 10:07
4
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:21) correct 39% (01:43) wrong based on 480 sessions

HideShow timer Statistics

A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probability that the number of women on the committee will increase?

(1) n + k = 12
(2) k/n = 1/3
[Reveal] Spoiler: OA

Last edited by tom09b on 17 Feb 2012, 04:19, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 36566
Followers: 7078

Kudos [?]: 93176 [3] , given: 10553

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

15 Feb 2012, 11:20
3
KUDOS
Expert's post
2
This post was
BOOKMARKED
A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?

Notice that the probability of selecting a woman from 4 alternates is 1/2.

Now, the number of women on the committee will increase if we replace a man from the committee with a woman from 4 alternates. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.

(1) n + k = 12. Not sufficient as we can not get the probability of selecting a man from the committee.
(2) k/n = 1/3 --> k/(k+n)=1/4. Sufficient.

_________________
Intern
Joined: 13 Feb 2012
Posts: 20
WE: Other (Transportation)
Followers: 0

Kudos [?]: 39 [0], given: 14

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

15 Feb 2012, 11:31
Bunuel wrote:
A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?

Notice that the probability of selecting a woman from 4 alternates is 1/2.

Now, the number of women on the committee will increase if we replace a man from the committee with a woman from 4 alternates. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.

(1) n + k = 12. Not sufficient as we can not get the probability of selecting a man from the committee.
(2) k/n = 1/3 --> k/(k+n)=1/4. Sufficient.

My intuition drove me to B, as well but.. I couldn't find the way! Thank you!!
Senior Manager
Joined: 19 Oct 2010
Posts: 271
Location: India
GMAT 1: 560 Q36 V31
GPA: 3
Followers: 7

Kudos [?]: 75 [1] , given: 27

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

03 Jul 2012, 08:40
1
KUDOS
Here is how I analyzed it if it helps:

The probability of selecting a woman from the alternates as given is - (2/4) = (1/2)
The probability of selecting a woman from the committee is - n/(n+k)

Now, we need to figure out the probability of pick a woman from the committee AND from the alternates [P(W&W)]. Therefore this is an AND problem.

1. n/12 Insufficient
2. k/n=1/3. Therefore n/(n+k)=3/4
Sufficient because P(W&W)=(3/4)*(1/2)
_________________

petrifiedbutstanding

Math Expert
Joined: 02 Sep 2009
Posts: 36566
Followers: 7078

Kudos [?]: 93176 [0], given: 10553

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

07 Jun 2013, 05:12
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on probability problems: math-probability-87244.html

All DS probability problems to practice: search.php?search_id=tag&tag_id=33
All PS probability problems to practice: search.php?search_id=tag&tag_id=54

Tough probability questions: hardest-area-questions-probability-and-combinations-101361.html

_________________
Intern
Joined: 09 Apr 2013
Posts: 32
Location: United States
Concentration: Social Entrepreneurship, Strategy
GMAT 1: 750 Q50 V41
GPA: 3.55
Followers: 1

Kudos [?]: 38 [3] , given: 0

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

07 Jun 2013, 08:17
3
KUDOS
1
This post was
BOOKMARKED
tom09b wrote:
A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?

(1) n + k = 12
(2) k/n = 1/3

Rewording of the question:
What is the probability that a man is chosen to be replaced and the alternate to replace him is a woman.

What you need is (probability of man chosen) x (probability of woman alternate)

$$\frac{k}{k+n} * \frac{2}{4} = \frac{k}{2(k+n)}$$

(1) n+k = 12
if n=1 and k=11, $$\frac{11}{2(12)} = \frac{11}{24}$$
if n=2 and k=10, $$\frac{10}{2(12)} = \frac{10}{24}$$
insufficient

(2) $$\frac{k}{n} = \frac{1}{3}$$
if k=1 and n=3, $$\frac{1}{2(4)} = \frac{1}{8}$$
if k=2 and n=6, $$\frac{2}{2(8)} = \frac{1}{8}$$; etc...
sufficient

Intern
Joined: 24 Dec 2012
Posts: 29
Concentration: Entrepreneurship, Social Entrepreneurship
WE: Design (Computer Software)
Followers: 0

Kudos [?]: 42 [0], given: 51

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

20 Mar 2014, 04:34
Bunuel wrote:
A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?

Notice that the probability of selecting a woman from 4 alternates is 1/2.

Now, the number of women on the committee will increase if we replace a man from the committee with a woman from 4 alternates. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.

(1) n + k = 12. Not sufficient as we can not get the probability of selecting a man from the committee.
(2) k/n = 1/3 --> k/(k+n)=1/4. Sufficient.

. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.
Math Expert
Joined: 02 Sep 2009
Posts: 36566
Followers: 7078

Kudos [?]: 93176 [0], given: 10553

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

20 Mar 2014, 04:57
tusharGupta1 wrote:
Bunuel wrote:
A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?

Notice that the probability of selecting a woman from 4 alternates is 1/2.

Now, the number of women on the committee will increase if we replace a man from the committee with a woman from 4 alternates. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.

(1) n + k = 12. Not sufficient as we can not get the probability of selecting a man from the committee.
(2) k/n = 1/3 --> k/(k+n)=1/4. Sufficient.

. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.

For the number of women on the committee to increase we must replace a man from the committee with a woman from 4 alternates.

The probability of selecting a man from the committee is (# of men in the committee)/(total # of people in the committee) = k/(k+n);
The probability of selecting a woman from 4 alternates is (# of women)/(total # of people) = 2/4 = 1/2.

Therefore, the probability that we select a man from the committee AND a woman from 4 alternates is k/(k+n)*1/2.

Hope it's clear.
_________________
Intern
Joined: 24 Dec 2012
Posts: 29
Concentration: Entrepreneurship, Social Entrepreneurship
WE: Design (Computer Software)
Followers: 0

Kudos [?]: 42 [0], given: 51

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

20 Mar 2014, 05:33
Bunuel wrote:
tusharGupta1 wrote:
Bunuel wrote:
A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?

Notice that the probability of selecting a woman from 4 alternates is 1/2.

Now, the number of women on the committee will increase if we replace a man from the committee with a woman from 4 alternates. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.

(1) n + k = 12. Not sufficient as we can not get the probability of selecting a man from the committee.
(2) k/n = 1/3 --> k/(k+n)=1/4. Sufficient.

. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.

For the number of women on the committee to increase we must replace a man from the committee with a woman from 4 alternates.

The probability of selecting a man from the committee is (# of men in the committee)/(total # of people in the committee) = k/(k+n);
The probability of selecting a woman from 4 alternates is (# of women)/(total # of people) = 2/4 = 1/2.

Therefore, the probability that we select a man from the committee AND a woman from 4 alternates is k/(k+n)*1/2.

Hope it's clear.

Thankx a ton ............................................................................................................................................................
Manager
Joined: 20 Oct 2013
Posts: 66
Followers: 0

Kudos [?]: 2 [0], given: 27

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

12 May 2014, 04:12
Bunuel wrote:
tusharGupta1 wrote:
Bunuel wrote:
A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?

Notice that the probability of selecting a woman from 4 alternates is 1/2.

Now, the number of women on the committee will increase if we replace a man from the committee with a woman from 4 alternates. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.

(1) n + k = 12. Not sufficient as we can not get the probability of selecting a man from the committee.
(2) k/n = 1/3 --> k/(k+n)=1/4. Sufficient.

. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.

For the number of women on the committee to increase we must replace a man from the committee with a woman from 4 alternates.

The probability of selecting a man from the committee is (# of men in the committee)/(total # of people in the committee) = k/(k+n);
The probability of selecting a woman from 4 alternates is (# of women)/(total # of people) = 2/4 = 1/2.

Therefore, the probability that we select a man from the committee AND a woman from 4 alternates is k/(k+n)*1/2.

Hope it's clear.

Dear Bunnel

Statement A: was clearly insufficient as we didnt know n & k individually.
statement B:
ratio of m:w = 1:3

so suppose, 1 m and 3 women r there in the committee

and if we replace the man with women, then the no. of women will increase.

now we have no man just 4 women..

probability of a new alternate as women in the committee: 3/4*1/2 = 3/8... lesser than 3/4

but if we replace the man with a man... there should be no change right as there will be 1 man and 3 women still
ans is diff therefore insufficient..

_________________

Hope to clear it this time!!
GMAT 1: 540
Preparing again

Math Expert
Joined: 02 Sep 2009
Posts: 36566
Followers: 7078

Kudos [?]: 93176 [0], given: 10553

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

12 May 2014, 07:53
nandinigaur wrote:

Dear Bunnel

Statement A: was clearly insufficient as we didnt know n & k individually.
statement B:
ratio of m:w = 1:3

so suppose, 1 m and 3 women r there in the committee

and if we replace the man with women, then the no. of women will increase.

now we have no man just 4 women..

probability of a new alternate as women in the committee: 3/4*1/2 = 3/8... lesser than 3/4

but if we replace the man with a man... there should be no change right as there will be 1 man and 3 women still
ans is diff therefore insufficient..

Don't understand what is your question...

The question asks what is the probability that the number of women on the committee will increase? The probability that the number of women on the committee will increase is k/(k+n)*1/2.

From (2) we get that k/(k+n)*1/2 = 1/4*1/2 = 1/8.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13451
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

31 Oct 2015, 11:44
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: 13 Sep 2015
Posts: 90
Location: United States
GMAT 1: 770 Q50 V45
GPA: 3.84
Followers: 2

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

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

01 Nov 2015, 12:56
unnecessary to get a number:

in order to increase the number of women, the only way is to replace a man with a woman

1. if a woman is replaced by a woman, the number will remain;

2. if a woman is replaced by a man, the number will decrease;

3. if a man is replaced by a man, the number will remain

so the possibility is:

(k/n+k)*(2/4), the key is the ratio of woman to man

(1) n+k=12, insufficient

(2)k/n=1/3, so k/n+k=1/4, sufficient

B
Manager
Joined: 06 Oct 2015
Posts: 60
Followers: 0

Kudos [?]: 3 [0], given: 29

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

17 Oct 2016, 07:01
Hi Bunuel,
Why does k/(k+n)*1/2 will represent the number of woman increase? How it relates to increment. Will you explain it?
Math Expert
Joined: 02 Sep 2009
Posts: 36566
Followers: 7078

Kudos [?]: 93176 [0], given: 10553

Re: A committee consists of n women and k men. In addition there [#permalink]

Show Tags

17 Oct 2016, 07:05
NaeemHasan wrote:
Hi Bunuel,
Why does k/(k+n)*1/2 will represent the number of woman increase? How it relates to increment. Will you explain it?

For the number of women on the committee to increase we must replace a man from the committee with a woman from 4 alternates.

The probability of selecting a man from the committee is (# of men in the committee)/(total # of people in the committee) = k/(k+n);
The probability of selecting a woman from 4 alternates is (# of women)/(total # of people) = 2/4 = 1/2.

Therefore, the probability that we select a man from the committee AND a woman from 4 alternates is k/(k+n)*1/2.

Hope it's clear.
_________________
Re: A committee consists of n women and k men. In addition there   [#permalink] 17 Oct 2016, 07:05
Similar topics Replies Last post
Similar
Topics:
28 A jury pool consists of 6 men and w women. If 2 jurors 16 13 Jan 2014, 10:26
2 A certain economics class consists of 50 women and 30 men. H 5 06 Oct 2013, 01:52
14 Four men and three women make up a seven-member committee 7 14 Jul 2013, 11:12
28 The ratio of the number of women to the number of men to the 13 28 Apr 2008, 12:24
3 A startting line up of a team consists of x men and y women. 10 17 Jan 2008, 09:42
Display posts from previous: Sort by