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

It is currently 12 Nov 2019, 22:32

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 13 Feb 2012
Posts: 14
WE: Other (Transportation)
A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post Updated on: 17 Feb 2012, 05:19
6
16
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

57% (01:59) correct 43% (02:00) wrong based on 514 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

Originally posted by tom09b on 15 Feb 2012, 11:07.
Last edited by tom09b on 17 Feb 2012, 05:19, edited 2 times in total.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58991
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 15 Feb 2012, 12:20
4
7
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.

Answer: B.
_________________
Most Helpful Community Reply
Current Student
avatar
B
Joined: 09 Apr 2013
Posts: 39
Location: United States (DC)
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '20 (A$)
GMAT 1: 750 Q50 V41
GPA: 3.55
WE: General Management (Non-Profit and Government)
Reviews Badge
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 07 Jun 2013, 09:17
4
3
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

Answer is B
General Discussion
Intern
Intern
avatar
Joined: 13 Feb 2012
Posts: 14
WE: Other (Transportation)
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 15 Feb 2012, 12:31
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.

Answer: B.


My intuition drove me to B, as well but.. I couldn't find the way! Thank you!!
Manager
Manager
avatar
Joined: 19 Oct 2010
Posts: 155
Location: India
GMAT 1: 560 Q36 V31
GPA: 3
GMAT ToolKit User
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 03 Jul 2012, 09:40
1
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
User avatar
V
Joined: 02 Sep 2009
Posts: 58991
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 07 Jun 2013, 06:12
1
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
Intern
avatar
Joined: 24 Dec 2012
Posts: 19
Concentration: Entrepreneurship, Social Entrepreneurship
WE: Design (Computer Software)
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 20 Mar 2014, 05:34
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.

Answer: B.


. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.
Please elaborate on this ..
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58991
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 20 Mar 2014, 05:57
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.

Answer: B.


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


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
Intern
avatar
Joined: 24 Dec 2012
Posts: 19
Concentration: Entrepreneurship, Social Entrepreneurship
WE: Design (Computer Software)
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 20 Mar 2014, 06:33
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.

Answer: B.


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


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 :-D ............................................................................................................................................................
Manager
Manager
avatar
Joined: 20 Oct 2013
Posts: 50
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 12 May 2014, 05:12
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.

Answer: B.


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


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.. :(

Please explain.
_________________
Hope to clear it this time!!
GMAT 1: 540
Preparing again :(
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58991
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 12 May 2014, 08:53
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.. :(

Please explain.


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.
_________________
Manager
Manager
avatar
Joined: 13 Sep 2015
Posts: 82
Location: United States
Concentration: Social Entrepreneurship, International Business
GMAT 1: 770 Q50 V45
GPA: 3.84
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 01 Nov 2015, 13:56
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
Manager
User avatar
S
Joined: 06 Oct 2015
Posts: 86
Location: Bangladesh
Concentration: Accounting, Leadership
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 17 Oct 2016, 08:01
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
User avatar
V
Joined: 02 Sep 2009
Posts: 58991
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 17 Oct 2016, 08:05
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.
_________________
Director
Director
User avatar
P
Joined: 14 Dec 2017
Posts: 510
Location: India
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 02 Jun 2018, 22:56
Given,
A committee of
n - women
k - men

Alternate choices, in case of replacement, available are 2 women & 2 men.

The probability of increasing the # of women, is by replacement of 1 man in the committee with 1 woman from the alternates.

Consider this as a selection of 2 people, one man from k men & one woman from the 2 alternates.

#of ways selecting 1 man from k men = k
#of way of selecting 1 woman from 2 women = 2

Required Probability = Probability of selecting 1 man from (n+k) members * Probability of selecting 1 woman from 4 alternates

Therefore required Probability is \({k/(n+k)}*{2/4}\)

Ok now lets check

Statement 1 : \(n+k = 12\), clearly not sufficient, as n=10, k= 2 or n=7, k=5, or many other combinations.

Statement 2: \(k/n =1/3\)

which is \(n/k = 3/1\)

By adding 1 to each side can be converted to

\((n+k)/k = 4/1\)

\(k/(n+k) = 1/4\)

Hence statement 2 is sufficient to find the required probability.
_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13575
Re: A committee consists of n women and k men. In addition there  [#permalink]

Show Tags

New post 11 Jun 2019, 19:31
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.
_________________
GMAT Club Bot
Re: A committee consists of n women and k men. In addition there   [#permalink] 11 Jun 2019, 19:31
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne