Hi pacifist85,
In this ratio question, we're dealing with numbers of employees. Since you CANNOT have a "fraction" of an employee, the ratio of 3:4:8 means that the number of employees at the first company MUST be a multiple of 3, the number at the second company MUST be an equivalent multiple of 4 and the number at the third company MUST be an equivalent multiple of 8.
So, we could have 3, 4 and 8 employees = 15 total
We could also have 6, 8 and 16 employees = 30 total
Etc.
In real basic terms, the total number of employees IS a positive multiple of 15. We just don't know WHICH positive multiple of 15.
We're asked if the average age of all the employees is UNDER 40. This is a YES/NO question.
Fact 1: Total age = 600
IF....
There are 15 employees, then the average age is 600/15 = 40 and the answer to the question is NO.
IF....
There are 30 employees, then the average age is 600/30 = 20 and the answer to the question is YES.
Fact 1 is INSUFFICIENT.
Fact 2: The average age at each company is 40, 20 and 50, respectively.
This information gives us an EXACT weighted average.
IF....
There are 15 employees, then the average is [3(40) + 4(20) + 8(50)]/15 = 600/15 = 40 and the answer to the question is NO.
Increasing the number of employees will NOT change the answer though, since the number of employees is based on the 3:4:8 ratio.
IF...
There are 30 employees, then the average is [6(40) + 8(20) + 16(50)]/30 = 1200/30 = 40 and the answer to the question is NO.
The answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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