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Resignations problem

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Resignations problem

by rupsk » Sat Jul 09, 2011 7:26 am
Currently, y percent of the members on the finance committee are women and next month, z percent of the men on the finance committee will resign. If no other personnel changes occur, then after the resignations next month, the men who remain on the finance committee will represent what percent of the total finance committee members?


(100)(100 - z)(100 - y)
_____________________
1002 - z(100 - y)


(100 - z)(100 - y)
_______________
100

(100 - z)(100 - y)


zy
________
100 - z


z(100 - y)
_________
100


I had applied below logic
Committee member = T
women member = Ty/100
men member = T-(Ty/100)
men remained after resignation= (1-(z/100))(100-y/100)T
so percentage is = ((100-z)/100)(100-y/100)*100
=(100-z)(100-y)/100

but this is not correct answer. Please tell me where I got wrong?
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by Frankenstein » Sat Jul 09, 2011 8:15 am
rupsk wrote: I had applied below logic
Committee member = T
women member = Ty/100
men member = T-(Ty/100)
men remained after resignation= (1-(z/100))(100-y/100)T
so percentage is = ((100-z)/100)(100-y/100)*100
=(100-z)(100-y)/100

but this is not correct answer. Please tell me where I got wrong?
Hi,
Denominator will not be T, As z% resigned, the total number of members remaining will be T - T(1-y/100)(z/100).
So percentage is 100*(1-(z/100))(100-y/100)T/T[1-(1-y/100)(z/100)]

Hence, A
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by rupsk » Sat Jul 09, 2011 8:26 am
Thanks a lot.
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by GMATGuruNY » Mon Jul 11, 2011 8:28 am
rupsk wrote:Currently, y percent of the members on the finance committee are women and next month, z percent of the men on the finance committee will resign. If no other personnel changes occur, then after the resignations next month, the men who remain on the finance committee will represent what percent of the total finance committee members?


A.(100)(100 - z)(100 - y) / 100^2 - z(100 - y)


B.(100 - z)(100 - y) / 100

C.(100 - z)(100 - y)

D.zy / 100 - z

E.z(100 - y) / 100


I had applied below logic
Committee member = T
women member = Ty/100
men member = T-(Ty/100)
men remained after resignation= (1-(z/100))(100-y/100)T
so percentage is = ((100-z)/100)(100-y/100)*100
=(100-z)(100-y)/100

but this is not correct answer. Please tell me where I got wrong?
Much easier to plug in numbers.

Let total = 100.
Let y = 50.
Since y=50% of the 100 members are women, women = 50, men = 50.
Let z = 50.
Thus, men who resign = .5*50 = 25.
Remaining men = 50-25 = 25.
Total members left = 100-25 = 75.
Men/Total = 25/75 = 33.33%. This is our target.

Now we plug y=50 and z=50 into the answers to see which yields our target of 33.33.

Only answer choice A works:
(100)(100 - z)(100 - y) / 100^2 - z(100 - y)
= 100(100-50)(100-50) / (100)(100) - 50(100-50)
= 100*50*50 / 100*100 - 50*50
= 100*50*50 / 50*50 (2*2 - 1)
= 100/3 = 33.33.

The correct answer is A.
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