percentage

seanceserene wrote:In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?

imo 80%

let mle=m
and female=f
total=m+f (t1)

now 50 percent of the male employees are at least 35 years old------>0.5 m
and 40 percent of the female employees are at least 35 years old----->0.4f

total employees >=35 yrs=0.5m+0.4f

now If 42 percent of all the employees are at least 35 years old--------> 0.42(m+f)=0.5m+0.4f

solving m=1/4(f)

total=5f/4

fraction reqd=f/[5f/4]=4/5=80%

seanceserene wrote:In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?

say the company has x fraction of females , 1-x fraction of males and the company has total D employees

(xD*0.4 + (1-x)D*0.5)/D = 0.42

x*0.4 + (1-x)*0.5 = .42

0.1x = 0.08
x= 0.8 or 80%

Female =y Male = x
0.42 (x+y)=0.5x+0.4y
0.02 y = 0.08 x or x/y = 1/4
y/x+y = 4/5

It is always important to set up problems in a way that most naturally chimes with the principles involved.

42% is the least number of male and Females who are 35 years old. So we have fraction of male plus fraction of female over Total number of make and female (M+F). This hardly requires much thinking and the algebra flows naturally from it.

(.5M + .4F)/(M+F) =.42

Solving this gives F= 4M

But we want F/Total and since we now know the relationship b/w F and M we can solve easily in terms of F. M = F/4
So Total = F + F/4 = 5F/4

F/5F/4 = 4/5=80%.

Algebra can get messy so you want to stick as close to the Fundamental Principles as possible. If you make an error in the algebra, your principles should put u back on track.

For example, you know from above the number of women is four times that of men men so you expect a high percent as your answer. Suppose u didn't know this and calculated some thing like 45% due to error and you see this in the answer choice. You would go for it.