M23-23

Official Solution:


If 25% of a company's employees are women older than 30, what percent of the men employees are 30 or younger?

Let's assume that there are a total of 100 employees in the company. Thus, there are 25 women who are older than 30.

(1) Half of the women employees are 30 or younger.

Hence, the remaining half of women employees are older than 30. Therefore, 25 women which are older than 30, account for half of the women employees, which means that there are \(2*25=50\) women employees and \(100-50=50\) men employees. But we still don't know how many from these 50 men are 30 or younger. Not sufficient.

(2) 35% of the company's employees are men of 30 or younger.

Hence, there 35 men who are 30 or younger. We still don't know the total number of men employees. Not sufficient.

(1)+(2) From (1) we have that there are total of 50 men employees and from (2) we have that 35 men are 30 or younger. Therefore, \(\frac{35}{50}*100=70 \%\) of the men employees are 30 or younger. Sufficient.


Answer: C