I’m having trouble figuring out if these two statements are enough to tell whether the overall average salary is below $55K. Any help?

Question

A certain company consists of three divisions, A, B, and C. Of the employees in the three divisions, the employees in Division C have the greatest average (arithmetic mean) annual salary. Is the average annual salary of the employees in the three divisions combined less than $55,000 ? 
1. The average annual salary of the employees in Divisions A and B combined is $45,000. 
2. The average annual salary of the employees in Division C is $55,000.

Shruti T · Accepted Answer

The trick here is to recognize this is a weighted average problem.
Statement 1 gives the average of A and B, but without knowing anything about Division C&rsquo;s size or average, you can&rsquo;t say where the total lands. For example, if C had a huge number of employees at high salaries, it could raise the overall average above $55K &mdash; so this isn&rsquo;t enough.
Statement 2 tells you Division C&rsquo;s average is exactly $55K, and also that C has the highest average. That means A and B must both be below $55K. So even if C balances things out at 55K, the combined average across all three divisions has to be under 55K. That makes this one sufficient by itself.
So the answer is B &mdash; only statement 2 works.

V Gupta · Answer

Statement 1 alone isn&rsquo;t enough because it gives an average for A and B, but we don&rsquo;t know anything about how many people are in Division C or what their average is. C could have way more employees with really high salaries and push the total above $55K &mdash; or very few, keeping it below.
Statement 2, though, is enough. If Division C&rsquo;s average is exactly $55,000, and it's still the highest of the three, that means A and B must be below $55K. So when you combine them, the weighted average across A, B, and C must be less than $55K. That&rsquo;s because the only division hitting $55K is C, and the others are dragging it down. So statement 2 alone is sufficient &mdash; answer is B.