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Currently, y percent of the members on the finance committee [#permalink]
08 Aug 2006, 11:21

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Difficulty:

45% (medium)

Question Stats:

63% (04:12) correct
38% (02:05) wrong based on 96 sessions

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

Current month:
Let total = 100
No. of females = y
No. of males = 100-y

Next month:
No of females = y
No of males = (100-y)*(100-z)/100
Total = y + (100-y)*(100-z)/100
= (100y + 100^2 - 100y -100z+yz)/100
= [100^2 - z(100-y)]/100

Re: PS: Finance committee [#permalink]
08 Aug 2006, 12:28

w = y
m = 100 - y
total = 100
m after z = (100 - y) - [z (100- y)/100] = (100-z)(100-y)/100
m (after z) as a % of total = [(100-z)(100-y)/100]/[{(100-y)(100-z)/100} + y] x [100]

after solviing for y and z: m (after z) as a % of total = [100 (100-z)(100-y)]/[(100^2 - z (100-y)]

its A. imo, plugging-in is best for such a tedious calculation.

Current month: Let total = 100 No. of females = y No. of males = 100-y

Next month: No of females = y No of males = (100-y)*(100-z)/100 Total = y + (100-y)*(100-z)/100 = (100y + 100^2 - 100y -100z+yz)/100 = [100^2 - z(100-y)]/100

Current month: Let total = 100 No. of females = y No. of males = 100-y

Next month: No of females = y No of males = (100-y)*(100-z)/100 Total = y + (100-y)*(100-z)/100 = (100y + 100^2 - 100y -100z+yz)/100 = [100^2 - z(100-y)]/100

Re: Currently, y percent of the members on the finance committee [#permalink]
18 Apr 2012, 14:46

Expert's post

Hi, I know this is an ancient thread but was just replying in response to one of Magoosh's users who had asked me to take a look.

The responses above are fine (check out ps-dahiya's). The thing with this problem is the algebraic solution is time-consuming and unwieldy. It is not that the users are missing a more elegant algebraic solution. The take away from a question such as this one - esp., if you want to answer it in under 2 minutes - is to plug in. @Jaynayak shows how to do so in his post.

Re: Currently, y percent of the members on the finance committee [#permalink]
16 Jan 2014, 15:00

Let's say that there are a total of 100 members Let's also say that y = 50 So there are 50 men Now z = 10 so 45 men are left (45/95)*100 = 9/19 *100 = 900/19

Now let's plug answer choices Target 900/19 Inputs y=50 z=10

Re: Currently, y percent of the members on the finance committee [#permalink]
16 Jan 2014, 19:40

Expert's post

jlgdr wrote:

Let's say that there are a total of 100 members Let's also say that y = 50 So there are 50 men Now z = 10 so 45 men are left (45/95)*100 = 9/19 *100 = 900/19

Now let's plug answer choices Target 900/19 Inputs y=50 z=10

Only A gives the correct answer

Hope it helps Cheers! J

Yes, number plugging is the best choice here though I would take much easier numbers to reduce the time taken. Almost no calculations will be involved.

e.g. Say 50% are women i.e. y = 50 and say 100% of men will resign i.e. z = 100 so the correct option should give me 0. I see that z = 100 is not a problem because you don't have z - 100 anywhere in the denominators. (A), (B) and (C) have z - 100 in the numerator so they will give us 0. (D) and (E) will not. So I will only worry about (A), (B) and (C).

Now say z = 50% i.e. the remaining men will be 25/75 = 1/3. Put z = 50 and y = 50 in (B) and (C) since they are simpler and you can just see what you will get without any calculations. Neither gives 33.33. Obviously, (A) will be the correct answer. You don't even need to plug in to check.