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# A committee is composed of w women and m men. If 3 women and

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Manager
Joined: 02 Dec 2012
Posts: 178
A committee is composed of w women and m men. If 3 women and [#permalink]

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20 Dec 2012, 06:30
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Question Stats:

91% (01:40) correct 9% (00:58) wrong based on 785 sessions

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A committee is composed of w women and m men. If 3 women and 2 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by

(A) w/m
(B) w/(w+m)
(C) (w+3)/(m+2)
(D) (w+3)/(w+m+3)
(E) (w+3)/(w+m+5)
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39597
Re: A committee is composed of w women and m men. If 3 women and [#permalink]

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20 Dec 2012, 06:32
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A committee is composed of w women and m men. If 3 women and 2 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by

(A) w/m
(B) w/(w+m)
(C) (w+3)/(m+2)
(D) (w+3)/(w+m+3)
(E) (w+3)/(w+m+5)

The total number of members on the enlarged committee is (w+3)+(m+2)=w+m+5;
The total number of women on the enlarged committee is w+3.

Thus, the probability that a woman is selected is P=favorable/total=(w+3)/(w+m+5).

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Concentration: Operations, Marketing
GMAT 1: 510 Q36 V25
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Re: A committee is composed of w women and m men. If 3 women and [#permalink]

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30 Dec 2013, 01:12
Bunuel,
Why is this incorrect ?

Let no of Women =10
Let no of Men =8
After addition of new ppl Women =13 , Men =10 , total =23

To select 1 woman out of the total (23)

$$13/23$$

On substituting in the answers B fits.
What am i doing wrong ?..
Math Expert
Joined: 02 Sep 2009
Posts: 39597
Re: A committee is composed of w women and m men. If 3 women and [#permalink]

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30 Dec 2013, 01:22
thinktank wrote:
Bunuel,
Why is this incorrect ?

Let no of Women =10
Let no of Men =8
After addition of new ppl Women =13 , Men =10 , total =23

To select 1 woman out of the total (23)

$$13/23$$

On substituting in the answers B fits.
What am i doing wrong ?..

If you substitute w=10 and m=8 in option B you get w/(w+m)=8/18 not 13/23, while option E gives (w+3)/(w+m+5)=13/23. Notice that w and m are the numbers of women and men BEFORE 3 women and 2 men were added to the committee.

Hope it's clear.
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Re: A committee is composed of w women and m men. If 3 women and [#permalink]

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30 Dec 2013, 01:58
Bunuel,
How can we assume that we have to use the initial number of men and women to calculate the final result. the question states that

'and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by'

So we have to find the possibility of choosing 1 Woman out of the total number of women (13) ie) $$13C1$$..Isnt that what the question means ??
Math Expert
Joined: 02 Sep 2009
Posts: 39597
Re: A committee is composed of w women and m men. If 3 women and [#permalink]

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30 Dec 2013, 02:01
thinktank wrote:
Bunuel,
How can we assume that we have to use the initial number of men and women to calculate the final result. the question states that

'and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by'

So we have to find the possibility of choosing 1 Woman out of the total number of women (13) ie) $$13C1$$..Isnt that what the question means ??

A committee is composed of W women and M men. Then 3 women and 2 men are added. W and M are initial numbers of women and men,
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Re: A committee is composed of w women and m men. If 3 women and [#permalink]

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14 Feb 2015, 16:03
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Re: A committee is composed of w women and m men. If 3 women and [#permalink]

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03 Apr 2015, 15:59
I solved based on the word enlarged and took it to mean the new total of people on the committee. Hence, ended up with answer B, but from your solution the question is asking for the probability of picking a woman from the initial group of people. Anyway to avoid this in the future?
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Re: A committee is composed of w women and m men. If 3 women and [#permalink]

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03 Apr 2015, 16:47
Hi All,

This question is perfect for TESTing VALUES.

We're told that a committee is composed of W women and M men.

IF...
W = 2
M = 3

3 women and 2 men are then ADDED to the committee.....

Women = 2+3 = 5
Men = 3+2 = 5

The question asks for the probability of selecting a woman from this larger group:

5 women and 10 total people --> 5/10

So we're looking for an answer that = 5/10 = 1/2 when W=2 and M=3

Answer A: 2/3 NOT a match
Answer B: 2/(2+3) = 2/5 NOT a match
Answer C: (2+3)/(3+2) = 5/5 NOT a match
Answer D: (2+3)/(2+3+3) = 5/8 NOT a match
Answer E: (2+3)/(2+3+5) = 5/10 This IS a match

[Reveal] Spoiler:
E

GMAT assassins aren't born, they're made,
Rich
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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 18 Feb 2015 Posts: 12 Re: A committee is composed of w women and m men. If 3 women and [#permalink] ### Show Tags 03 Apr 2015, 18:27 EMPOWERgmatRichC wrote: Hi All, This question is perfect for TESTing VALUES. We're told that a committee is composed of W women and M men. IF... W = 2 M = 3 3 women and 2 men are then ADDED to the committee..... Women = 2+3 = 5 Men = 3+2 = 5 The question asks for the probability of selecting a woman from this larger group: 5 women and 10 total people --> 5/10 So we're looking for an answer that = 5/10 = 1/2 when W=2 and M=3 Answer A: 2/3 NOT a match Answer B: 2/(2+3) = 2/5 NOT a match Answer C: (2+3)/(3+2) = 5/5 NOT a match Answer D: (2+3)/(2+3+3) = 5/8 NOT a match Answer E: (2+3)/(2+3+5) = 5/10 This IS a match Final Answer: [Reveal] Spoiler: E GMAT assassins aren't born, they're made, Rich Thanks Rich! I used TEST IT, and those exact figures. Where I went wrong was using the total number of women (5) and men (5) to solve since the question asked for enlarged which I took to mean all/total. How do I avoid this trap in the future? Practice? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9254 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: A committee is composed of w women and m men. If 3 women and [#permalink] ### Show Tags 04 Apr 2015, 11:56 Hi MBA18, After reading your 2 posts, I'm not exactly sure what you're asking. You ARE supposed to use the ENLARGED group (M+W+3+2) to get the correct answer. The questions that you'll face on the Official GMAT are always carefully worded to make sure that there's no mis-understanding (or 'bias') on the part of the Test Taker. Here, the prompt tells us that the 5 people are added and then asks for the probability of selecting a woman from the ENLARGED group - that's a clear set of 'instructions.' You might find some practice problems that are not written in such a meticulous fashion, but that's okay. There will always be some inconsistencies in how GMAT companies design their materials. The big 'takeaway' is that you were strategic about how you approached the prompt - keep thinking in THAT way, and your scores should improve. 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

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Re: A committee is composed of w women and m men. If 3 women and [#permalink]

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07 Jun 2016, 12:41
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.
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Re: A committee is composed of w women and m men. If 3 women and [#permalink]

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28 Jun 2016, 05:38
A committee is composed of w women and m men. If 3 women and 2 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by

(A) w/m
(B) w/(w+m)
(C) (w+3)/(m+2)
(D) (w+3)/(w+m+3)
(E) (w+3)/(w+m+5)

To solve the problem we must remember that:

probability = (number of favorable outcomes)/(total number of outcomes)
In the problem we are being asked for the probability of a woman being selected.

favorable outcomes = a woman being selected

number of favorable outcomes = w + 3

We see that we started with w women and then 3 women were added.

total outcomes = total people in the committee

number of total outcomes = w + 3 + m + 2 = w + m + 5

We see that we started with w women and then 3 women were added, and we started with m men and 2 men were added. Thus the probability of a woman being selected is:

(w + 3)/(w + m + 5)

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Re: A committee is composed of w women and m men. If 3 women and   [#permalink] 28 Jun 2016, 05:38
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