Bunuel wrote:

In the department of Mathematics at Green University, more than half of the professors have an income in excess of $80,000 a year. Which of the following cannot be the average (arithmetic mean) annual income of the professors in the department?

A. $160,000

B. $120,000

C. $50,000

D. $45,000

E. $40,000

The question can be answered by making two simple observations:

1) The question gives us a lower limit for the income of some of the professors, but no upper limit. Therefore, if some value in the answer choices is not a possibility for the average annual income, it must be because it is too low.

2) If one value is not a possibility for the average annual income, than any value smaller than that is also not possible.

Since there can be only one answer choice, it must be the smallest value provided in the answer choices, which is $40,000.

Alternate Solution:

Let’s consider an extreme case where there are 20 professors, 11 of which earn $80,001 and 9 of which earn $0. In this case, the average salary will be (80,001 x 11)/20 = 880,011 / 20 ≈ 44,000. As we can see, anything greater than or equal to $45,000 is possible, which leaves $40,000 as the only remaining answer choice.

Answer: E

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Jeffery Miller

Head of GMAT Instruction

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