nades09 wrote:

In a 200 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?

A. 49

B. 47

C. 45

D. 43

E. 41

There are men and women in 200 member association.

20% of men are homeowners and 25% of women are homeowners.

Let n be the number of men and 200-n be the number of women

So, 0.2 * n + .25 * (200-n) = n/5 + (200-n)/4 are homeowners

Now both the parameters must be an integer. Also we need to find the least number of homeowners so we need to maximize the number of men i.e. n as only 20% of men are homeowners.

So, Lets tart taking such values

First such value is (200,0) but number of women can't be 0

2nd such value is (180,20)

So, no. of homeowners = 180/5 +20/4 = 36 +5 = 41.

If we further find the values which satisfies the expression n/5 + (200-n)/4, we will find the value n/5 + (200-n)/4 increasing since the percentage of females who are homeowners > Percentage of male who are homeowners. And hence increase in no. of women will increase the number of homeowners.

Answer E
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