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

 It is currently 30 Aug 2015, 16:55

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

Kudos [?]: 18 [2] , given: 14

A committee consists of n women and k men. In addition there [#permalink]  15 Feb 2012, 10:07
2
KUDOS
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:17) correct 36% (01:38) wrong based on 322 sessions
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: 29151
Followers: 4729

Kudos [?]: 49823 [1] , given: 7498

Re: A committee consists of n women and k men. In addition there [#permalink]  15 Feb 2012, 11:20
1
KUDOS
Expert's post
1
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 [?]: 18 [0], given: 14

Re: A committee consists of n women and k men. In addition there [#permalink]  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: 272
Location: India
GMAT 1: 560 Q36 V31
GPA: 3
Followers: 6

Kudos [?]: 50 [1] , given: 27

Re: A committee consists of n women and k men. In addition there [#permalink]  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: 29151
Followers: 4729

Kudos [?]: 49823 [0], given: 7498

Re: A committee consists of n women and k men. In addition there [#permalink]  07 Jun 2013, 05:12
Expert's post
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: 31
Location: United States
Concentration: Strategy, Technology
GMAT 1: 750 Q50 V41
GPA: 3.55
Followers: 1

Kudos [?]: 22 [1] , given: 0

Re: A committee consists of n women and k men. In addition there [#permalink]  07 Jun 2013, 08:17
1
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: 30
Concentration: Entrepreneurship, Social Entrepreneurship
WE: Design (Computer Software)
Followers: 0

Kudos [?]: 21 [0], given: 51

Re: A committee consists of n women and k men. In addition there [#permalink]  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: 29151
Followers: 4729

Kudos [?]: 49823 [0], given: 7498

Re: A committee consists of n women and k men. In addition there [#permalink]  20 Mar 2014, 04:57
Expert's post
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: 30
Concentration: Entrepreneurship, Social Entrepreneurship
WE: Design (Computer Software)
Followers: 0

Kudos [?]: 21 [0], given: 51

Re: A committee consists of n women and k men. In addition there [#permalink]  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 [?]: 0 [0], given: 27

Re: A committee consists of n women and k men. In addition there [#permalink]  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: 29151
Followers: 4729

Kudos [?]: 49823 [0], given: 7498

Re: A committee consists of n women and k men. In addition there [#permalink]  12 May 2014, 07:53
Expert's post
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.
_________________
Re: A committee consists of n women and k men. In addition there   [#permalink] 12 May 2014, 07:53
Similar topics Replies Last post
Similar
Topics:
20 A jury pool consists of 6 men and w women. If 2 jurors 14 13 Jan 2014, 10:26
1 A certain economics class consists of 50 women and 30 men. H 5 06 Oct 2013, 01:52
6 Four men and three women make up a seven-member committee 6 14 Jul 2013, 11:12
13 The ratio of the number of women to the number of men to the 12 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