Bunuel wrote:

Five students took an exam. The average grade on the exam was 80. What was the median grade?

(1) The average of the two highest grades was 95.

(2) The average of the two lowest grades was 65.

The answer is C as follows.

Let the 5 grades are a, b, c, d, e increasing order

As per the question \(\frac{(a+b+c+d+e)}{5}\) = 80 => a+b+c+d+e = 400 ------------------Equation 1

(1) The average of the two highest grades was 95.

\(\frac{(d+e)}{2}\) = 95 => d+e = 190 ----------------------------------------------------------Equation 2

Since we do not know the values of values of a, b, c

Hence, INSUFFICIENT.

(2) The average of the two lowest grades was 65.[/quote]

\(\frac{(a+b)}{2}\) = 65 => a+b = 130 -----------------------------------------------------------Equation 3

Since we do not know the values of values of c, d, e

Hence, INSUFFICIENT.

Combining both and putting the values of a+b and d+e from equation 2 and 3 into equation 1 we get

a+b+c+d+e = 400 => 130+c+190 = 400 => c=80

c=80

Median of a series of numbers is the middle term when sorted in ascending or descending order.

Since we already assumed in the starting of the solution that the numbers a, b, c, d, e are in ascending order and we have also got the c=80, which is the middle term of this set of numbers.

Hence, SUFFICIENT

C is the answer.

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