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

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Joined: 02 Dec 2012
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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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Difficulty:

5% (low)

Question Stats:

93% (00:57) correct 7% (01:14) wrong based on 890 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)
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Joined: 02 Sep 2009
Posts: 60687
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
2
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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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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: 60687
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 ??
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Joined: 02 Sep 2009
Posts: 60687
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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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

GMAT assassins aren't born, they're made,
Rich
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Posts: 12
Re: A committee is composed of w women and m men. If 3 women and  [#permalink]

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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

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

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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
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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]

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13 May 2019, 11:20
Top Contributor
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)

A committee is composed of w women and m men. If 3 women and 2 men are added to the committee . . .
After the 3 women and 2 men are added, we have...
w+3 women and m+2 men

. . . and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by
P(select woman) = (# of women in committee)/(TOTAL # of people on committee)
= (w+3)/(w+3 + m+2 )
= (w+3)/(w+m+5)

Cheers,
Brent
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Re: A committee is composed of w women and m men. If 3 women and   [#permalink] 13 May 2019, 11:20
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