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# Currently, y percent of the members on the finance committee

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8399
Location: Pune, India
Re: Currently, y percent of the members on the finance committee  [#permalink]

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30 Dec 2017, 23:28
Shrish_nayak wrote:
VeritasPrepKarishma wrote:
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

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.

Hello Karishma,

Unfortunately, I am not getting the correct answer. I tried the below:

total = 20 people
women = 10 men=10 z%=10

so 10*10/100=1 hence remaining men = 9

total is 9/19*100 = 900/19

A. 100(100−10)(100−10)
-------------------------- = 100*90*90/10000-900= 810000/9100 = 8100/91
100^2−10(100−10)

Can you help me where did I go wrong with this one? VeritasPrepKarishma

Best Regards,
Shrish

How are y and z both 10?
If you have assumed that there are total 20 people of which 10 are men and 10 are women, it means y = 50 (the percentage of women)
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Karishma
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Joined: 24 Jul 2018
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Currently, y percent of the members on the finance committee  [#permalink]

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02 Aug 2018, 19:22
u2lover 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. $$\frac{100(100 - z)(100 - y)}{100^2 - z(100 - y)}$$

B. $$\frac{(100 - z)(100 - y)}{100}$$

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

D. $$\frac{zy}{100} - z$$

E. $$\frac{z(100 - y)}{100}$$

Came across this problem today. Plugging numbers in is obviously the fast method, but I'll leave an algebraic solution here in case someone's curious:

Note: Total refers to the whole committee.
Currently:
Women = y% of Total
Men = 1 - y% of Total

Next month:
z% of Men leave
=> 1 - z% of Men remain
=> (1 - z%)(1 - y%) of old Total remain

=> Number of men who remain divided by new Total:
(1 - z%)(1 - y%)/[y% + (1 - z%)(1 - y%)]

Multiply by 100/100:
Numerator = (100 - z)(100 - y)
Denominator = y + (100 - z)(1 - y%)

Continue multiplying by 100/100:
Numerator = 100(100 - z)(100 - y)
Denominator = 100y + (100 - z)(100 - y) = 100y + 100^2 - 100y - 100z + yz = 100^2 - 100z + yz = 100^2 - z(100 - y)

In form of fraction, we'll have:
$$\frac{100(100 - z)(100 - y)}{100^2 - z(100 - y)}$$

=> A
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"Experts who acknowledge the full extent of their ignorance may expect to be replaced by more confident competitors, who are better able to gain the trust of clients. An unbiased appreciation of uncertainty is a cornerstone of rationality—but it is not what people and organizations want." - Daniel Kahnemen

Currently, y percent of the members on the finance committee &nbs [#permalink] 02 Aug 2018, 19:22

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