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

_________________

"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