It is currently 18 Oct 2017, 04:19

### 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 of 2 people is to be formed from a group of 8

Author Message
TAGS:

### Hide Tags

Intern
Joined: 27 Sep 2010
Posts: 27

Kudos [?]: 87 [7], given: 3

A committee of 2 people is to be formed from a group of 8 [#permalink]

### Show Tags

22 Jan 2011, 03:06
7
KUDOS
21
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

37% (02:05) correct 63% (02:42) wrong based on 753 sessions

### HideShow timer Statistics

A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men. If P is the probability that both the selected people are men, is P > 0.25?

(1) More than 40% of the employees are men.
(2) The probability that both the selected people will be women is more than 20%.
[Reveal] Spoiler: OA

Kudos [?]: 87 [7], given: 3

Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128685 [7], given: 12182

Re: A committee of 2 people, is P > 0.25? [#permalink]

### Show Tags

22 Jan 2011, 03:32
7
KUDOS
Expert's post
15
This post was
BOOKMARKED
MichelleSavina wrote:
Q) A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men. If P is the probability that both the selected people are men, is P > 0.25?
(1) More than 40% of the employees are men.
(2) The probability that both the selected people will be women is more than 20%.

Given: $$m+w=8$$. Question: is $$\frac{m}{8}*\frac{m-1}{7}>\frac{1}{4}$$? --> is $$m(m-1)>14$$ --> is $$m\geq{5}$$? So the question basically asks whether the # of men in 8 people is more than or equal to 5 (5, 6, or 7).

(1) More than 40% of the employees are men --> $$m>0.4*8$$ --> $$m>3.2$$: there may be 4 men and in this case the answer to the question will be NO or there may be more than 4 men (5, 6, ...) and in this case the answer to the question will be YES. Not sufficient.

(2) The probability that both the selected people will be women is more than 20% -> $$\frac{w}{8}*\frac{w-1}{7}>\frac{1}{5}$$ --> $$w(w-1)>11.2$$ --> is $$w\geq{4}$$: there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 4, 3, ... So answer to the question whether there are more than or equal to 5 men is NO. Sufficient.

_________________

Kudos [?]: 128685 [7], given: 12182

Intern
Joined: 18 Oct 2011
Posts: 1

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

Re: A committee of 2 people is to be formed [#permalink]

### Show Tags

19 May 2012, 09:39
gmihir wrote:
A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men.If P is the probability that both the selected people are men, is P > 0.25?
(1) More than 40% of the employees are men.
(2) The probability that both the selected people will be women is more than 20%.

This is my first answer here... so I dont know how to use maths symbols here...

Probability that both men are selected is MC2/8C2. We have to find whether this is greater than 1/4.
If you solve : MC2/8C2 > 1/4, it gives you M^2 - M - 14 >0 which is true for M > 4.

So the first option is ruled out because 40% of 8 is 3.2, which means M can either 4 or greater than 4.

2. If you solve the second option, WC2/8C2 > 1/2, it gives W^2 - W- 11 > 0, which is true for W >= 4. Since total people are 8, M <= 4.

Hope its clear.

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

Manager
Joined: 16 May 2011
Posts: 71

Kudos [?]: 18 [0], given: 2

Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

### Show Tags

20 May 2012, 10:48
(2) The probability that both the selected people will be women is more than 20% -> \frac{w}{8}*\frac{w-1}{7}>\frac{1}{5} --> w(w-1)>11.2 --> is w\geq{4}: there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 4, 3, ... So answer to the question whether there are more than or equal to 5 men is NO. Sufficient.

can you explain what this equaiton means? W(W-1) >11.2 How do we know its SUFF by this equation?

Kudos [?]: 18 [0], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128685 [0], given: 12182

Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

### Show Tags

20 May 2012, 11:27
gmihir wrote:
A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men. If P is the probability that both the selected people are men, is P > 0.25?

(1) More than 40% of the employees are men.
(2) The probability that both the selected people will be women is more than 20%.

Merging similar topics. Please refer to the solution above.

dchow23 wrote:
(2) The probability that both the selected people will be women is more than 20% -> \frac{w}{8}*\frac{w-1}{7}>\frac{1}{5} --> w(w-1)>11.2 --> is w\geq{4}: there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 4, 3, ... So answer to the question whether there are more than or equal to 5 men is NO. Sufficient.

can you explain what this equaiton means? W(W-1) >11.2 How do we know its SUFF by this equation?

The question asks whether the # of men in 8 people is more than or equal to 5 (5, 6, or 7). From (2) we have that $$w(w-1)>11.2$$. Now, if the # of women is 3 then 3(3-1)=6<11.2, so w>3, which means that there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 8-4=4, 8-5=3, ... So, the answer to the question whether there are more than or equal to 5 men is NO.

Hope it's clear.
_________________

Kudos [?]: 128685 [0], given: 12182

Manager
Affiliations: Project Management Professional (PMP)
Joined: 30 Jun 2011
Posts: 198

Kudos [?]: 83 [0], given: 12

Location: New Delhi, India
Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

### Show Tags

15 Jun 2012, 03:07
Good question and great explanation... thanks
_________________

Best
Vaibhav

If you found my contribution helpful, please click the +1 Kudos button on the left, Thanks

Kudos [?]: 83 [0], given: 12

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16715

Kudos [?]: 273 [0], given: 0

Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

### Show Tags

17 Feb 2014, 05:40
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.
_________________

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16715

Kudos [?]: 273 [0], given: 0

Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

### Show Tags

01 Apr 2015, 07:29
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.
_________________

Kudos [?]: 273 [0], given: 0

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 9970

Kudos [?]: 3406 [1], given: 172

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

### Show Tags

01 Apr 2015, 20:38
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
Hi All,

There are a couple of ways to approach this question, depending on how comfortable you are with the math concepts involved. There's a great 'brute force' element to the question that you can take advantage of (as long as you write everything down and label your work).

We're told that we have a group of 8 people (some men and some women). We're told to randomly select 2 of the 8 people and we're asked if the probability that they're BOTH men is greater than .25 This is a YES/NO question.

Since there are only 8 people, we can have from 0 - 8 men in the group. We can do a bit of work up-front so that we can move faster through the two Facts later. We want to figure out the point at which the probability will be > .25

IF....
There are 4 men and 4 women
Probability of selecting 2 men is (4/8)(3/7) = 3/14
Since 3/12 = .25, 3/14 must be LESS than .25 (since the denominator of that fraction is bigger than 12)

IF.....
There are 5 men and 3 women
Probability of selecting 2 men is (5/8)(4/7) = 5/14
Since 5/15 = .333333, 5/14 must be BIGGER than .3333 (since the denominator of that fraction is smaller than 15)

So, with 4 OR FEWER men, the answer to the question is NO
With 5 OR MORE men, the answer to the question is YES

We now know that the question is really asking if the number of men is 5 OR GREATER. Again, this is a YES/NO question.

Fact 1: MORE than 40% of the employees are men.

(.4)(8) = 3.2, BUT since we CANNOT have a "fraction" of a man, we must have 4 OR MORE men....

IF...we have 4 men, then the answer to the question is NO
IF...we have 5 men, then the answer to the question is YES
Fact 1 is INSUFFICIENT

(2) The probability that both the selected people will be women is more than 20%.

For this Fact, we can use the calculations that we did at the beginning (with a little extra work).

IF....
There are 4 women and 4 men
Probability of selecting 2 women is (4/8)(3/7) = 3/14
Since 3/15 = .2, 3/14 must be GREATER than .2 (since the denominator of that fraction is less than 15)

This tells us that we have 4 OR MORE women.

IF... we have 4 women, then the answer to the question is NO
IF... we have MORE women, we have even FEWER men and the answer to the question is still NO.
Fact 2 is SUFFICIENT

[Reveal] Spoiler:
B

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3406 [1], given: 172

Intern
Joined: 18 May 2014
Posts: 35

Kudos [?]: 38 [1], given: 204

GMAT 1: 680 Q49 V35
Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

### Show Tags

18 May 2015, 04:10
1
KUDOS
Bunuel wrote:
MichelleSavina wrote:
Q) A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men. If P is the probability that both the selected people are men, is P > 0.25?
(1) More than 40% of the employees are men.
(2) The probability that both the selected people will be women is more than 20%.

Given: $$m+w=8$$. Question: is $$\frac{m}{8}*\frac{m-1}{7}>\frac{1}{4}$$? --> is $$m(m-1)>14$$ --> is $$m\geq{5}$$? So the question basically asks whether the # of men in 8 people is more than or equal to 5 (5, 6, or 7).

(1) More than 40% of the employees are men --> $$m>0.4*8$$ --> $$m>3.2$$: there may be 4 men and in this case the answer to the question will be NO or there may be more than 4 men (5, 6, ...) and in this case the answer to the question will be YES. Not sufficient.

(2) The probability that both the selected people will be women is more than 20% -> $$\frac{w}{8}*\frac{w-1}{7}>\frac{1}{5}$$ --> $$w(w-1)>11.2$$ --> is $$w\geq{4}$$: there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 4, 3, ... So answer to the question whether there are more than or equal to 5 men is NO. Sufficient.

Hi Bunuel

Why is ,the total number of ways in which 2 people can be selected , 8*7 and not 8C2?
that would mean we are taking order into consideration!
For ex : out of 4 people A B C D

ways of choosing 2 people - to form a committee - is 4C2 = 6
AB AC AD BC BD CD

and not 4*3 => which is 12 and will include the reverse as well since there isn't any position or order mentioned here while forming the committee.

Kudos [?]: 38 [1], given: 204

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 746

Kudos [?]: 2076 [2], given: 123

Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

### Show Tags

18 May 2015, 04:48
2
KUDOS
Expert's post
Anu26 wrote:
Bunuel wrote:
MichelleSavina wrote:
Q) A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men. If P is the probability that both the selected people are men, is P > 0.25?
(1) More than 40% of the employees are men.
(2) The probability that both the selected people will be women is more than 20%.

Given: $$m+w=8$$. Question: is $$\frac{m}{8}*\frac{m-1}{7}>\frac{1}{4}$$? --> is $$m(m-1)>14$$ --> is $$m\geq{5}$$? So the question basically asks whether the # of men in 8 people is more than or equal to 5 (5, 6, or 7).

(1) More than 40% of the employees are men --> $$m>0.4*8$$ --> $$m>3.2$$: there may be 4 men and in this case the answer to the question will be NO or there may be more than 4 men (5, 6, ...) and in this case the answer to the question will be YES. Not sufficient.

(2) The probability that both the selected people will be women is more than 20% -> $$\frac{w}{8}*\frac{w-1}{7}>\frac{1}{5}$$ --> $$w(w-1)>11.2$$ --> is $$w\geq{4}$$: there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 4, 3, ... So answer to the question whether there are more than or equal to 5 men is NO. Sufficient.

Hi Bunuel

Why is ,the total number of ways in which 2 people can be selected , 8*7 and not 8C2?
that would mean we are taking order into consideration!
For ex : out of 4 people A B C D

ways of choosing 2 people - to form a committee - is 4C2 = 6
AB AC AD BC BD CD

and not 4*3 => which is 12 and will include the reverse as well since there isn't any position or order mentioned here while forming the committee.

Dear Anu26

You're absolutely right.

The probability of selecting 2 men in the group = (No. of ways in which 2 men can be selected)/(No. of ways in which 2 people can be selected)

=mC2/8C2

= $$\frac{m(m-1)}{8*7}$$ (Since both mC2 and 8C2 contain 2!, it cancels out to give us this expression)

Hope this helped!

Regards

Japinder
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2076 [2], given: 123

Intern
Joined: 18 May 2014
Posts: 35

Kudos [?]: 38 [1], given: 204

GMAT 1: 680 Q49 V35
A committee of 2 people is to be formed from a group of 8 [#permalink]

### Show Tags

18 May 2015, 05:08
1
KUDOS
Ah ok right! Thanks. I didn't see m(m-1) in the numerator in the solution. Just jumped to why is it 8*7

So then with numbers starting 4 - considering statement 1) - with men=4 -> P = 4C2/8C2 = 6/28 , P <0.25

and then with 5 men -> P = 5C2/8C2 = 10/28 ,P>0.25 so that tells me how it is insufficient!

Thanks much. +1 to you!

Kudos [?]: 38 [1], given: 204

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16715

Kudos [?]: 273 [0], given: 0

Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

### Show Tags

16 Nov 2016, 10:25
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.
_________________

Kudos [?]: 273 [0], given: 0

Intern
Joined: 23 Jan 2016
Posts: 2

Kudos [?]: [0], given: 20

Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

### Show Tags

13 Jan 2017, 12:40
how is m(m−1)>14--> is m≥5??
Can anyone please elaborate the calculation?
_________________

stop complaining.. start doing...

Kudos [?]: [0], given: 20

Re: A committee of 2 people is to be formed from a group of 8   [#permalink] 13 Jan 2017, 12:40
Display posts from previous: Sort by