Bunuel wrote:

Which of the following is always true?

(I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.

(II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.

(III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.

A. I and III

B. I, II and III

C. II

D. I and II

E. None

IMO B

The average (arithmetic mean) of

five negative consecutive integers is equal to the average of the largest and smallest of them.

(-10+-9+-8+-7+-6)/5 = -40/5 = -8 same as (-10+-6)/2 = -8

TrueThe average (arithmetic mean) of

four positive consecutive integers is equal to the average of the largest and smallest of them.

(2+3+4+5)/4 = 14/4 same as (5+2)/2 = 7/2

always true(1+2+3+4)/4 = 10/4 same as (4+1)/2 = 5/2

The average (arithmetic mean) of

five consecutive integers is equal to the average of the largest and smallest of them.

(3+4+5+6+7)/5 = 5 same as (7+3)/2 = 5

TrueHence B