Is the average (arithmetic mean) of the numbers x, y, and z greater than z

Is the average (arithmetic mean) of the numbers x, y, and z greater than z?

  1. z - x < y - z
  2. x < z < y

Answer

Assume: (x + y + z)/3  > z

x + y + z > 3z

x + y > 2z

If the value of x + y is greater than 2z, then the average of x, y, and z is greater than z.

Statement 1: z - x < y - z

x + y > z + z

x + y > 2z

Hence, statement 1 is sufficient to answer the question.

Statement 2: x < z < y

From this statement, you cannot say whether x + y > 2z or not. Hence, statement 2 is not sufficient to answer the question.

The correct option is A.