At a certain company, 40% of the women are over 50 years old and 50% of the men are over 50 years old...

[BTGmoderatorLU]

Source: Veritas Prep

At a certain company, 40% of the women are over 50 years old and 50% of the men are over 50 years old. What percentage of the company are men?

1) 42% of all employees are over 50 years old
2) There are 500 employees at the company

The OA is A

[GMATGuruNY]

Source: Veritas Prep

At a certain company, 40% of the women are over 50 years old and 50% of the men are over 50 years old. What percentage of the company are men?

1) 42% of all employees are over 50 years old
2) There are 500 employees at the company

This is a WEIGHTED AVERAGE/MIXTURE problem.

Statement 1:
Women's percentage = 40%
Men's percentage = 50%
Percentage for the MIXTURE of all employees = 42%

To determine the ratio of women to men, use ALLIGATION -- a very efficient way to handle mixture problems.

Step 1: Plot the 3 percentages on a number line, with the percentages for women and men (40% and 50%) on the ends and the percentage for the mixture (42%) in the middle.
W 40---------42---------M 50

Step 2: Calculate the distances between the percentages.
W 40 ----2----42----8----M 50

Step 3: Determine the ratio in the mixture.
The ratio of women to men is equal to the RECIPROCAL of the distances in red.
W:M = 8:2 = 4:1

Of every 5 employees, 4 are women and 1 is a man, implying that men/total = 1/5 = 20%.
SUFFICIENT.

Statement 2:
No way to determine men/total.
INSUFFICIENT.

The correct answer is A.

Another alligation problem:
https://www.beatthegmat.com/mixture-prob ... tml#593241