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

Question

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)

Show Answer

Official Answer

E

(A) w/m

(B) w/(w+m)

(C) (w+3)/(m+2)

(D) (w+3)/(w+m+3)

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

Bunuel · Accepted Answer

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).

Answer: E.

thinktank · Answer

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 ?..

Bunuel · Answer

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.

thinktank · Answer

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 ??

Bunuel · Answer

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,

EMPOWERgmatRichC · Answer

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:  E

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

MBA18 · Answer

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?

EMPOWERgmatRichC · Answer

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

ScottTargetTestPrep · Answer

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)

The answer is E.

BrentGMATPrepNow · Answer

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)

Answer: E

Cheers,
Brent

100mitra · Answer

Correct option E
Total women added : (w+3)
Total of women and men added : (w+m+5)
P(W) =  (w+3)  /  (w+m+5)

ArnauG · Answer

Initially, the committee has w women and m men, making a total of w + m members.

After adding 3 women and 2 men, the committee has a total of w + 3 women and m + 2 men, making a total of (w + 3) + (m + 2) = w + m + 5 members.

The probability of selecting a woman from the enlarged committee is the ratio of the number of women to the total number of members.

Therefore, the probability can be represented as (w + 3) / (w + m + 5), which corresponds to option (E).

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

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