We can solve this using the Double Matrix method

Keep the word count down to a minimum, let's refer to the employees earning more than or equal to $100,000 a year as RICH employees, and refer to the other employees as POOR employees.


Let x = the total number of RICH employees
Let y = the total number of POOR employees
So, x+y = the TOTAL number of employees

This also means 0.85x = the number of RICH employees participating in the program
And 0.77y = the number of POOR employees participating in the program

We get the following:


Key concept: 0.85x and 0.77y must be POSITIVE INTEGERS

0.85x = (85/100)x = (17/20)x = 17x/20
If 17x/20 is a POSIIVE INTEGER, then x must be a multiple of 20

0.77y = (77/100)y = 77y/100
If 77y/100 is a POSIIVE INTEGER, then y must be a multiple of 100

Since x+y = the TOTAL number of employees, we're looking for answers choices such that the total number of employees can be expressed as (some positive multiple of 20) + (some positive multiple of 100)

A) 100 --> we can't rewrite 100 in the form (some positive multiple of 20) + (some positive multiple of 100)
B) 200 = (5)(20) + (1)(100) GREAT!
C) 350 --> we can't rewrite 350 in the form (some positive multiple of 20) + (some positive multiple of 100)
D) 460 = (3)(20) + (4)(100) GREAT!
E) 525 --> we can't rewrite 525 in the form (some positive multiple of 20) + (some positive multiple of 100)
F) 640 = (2)(20) + (6)(100) GREAT!
G) 750 --> we can't rewrite 750 in the form (some positive multiple of 20) + (some positive multiple of 100)
H) 880 = (4)(20) + (8)(100) GREAT!

Answer: B, D, F, H

Cheers,
Brent