GRE® Quant Practice | Statistics & Averages #2

GRE Sample Questions | Arithmetic Mean - Minimum Possible Average

The GRE maths sample question given below is a problem solving question in statistics. It tests two concepts : number systems and computing minimum average.

Question 2 : The average (arithmetic mean) of two numbers x and y is 15. If x, y, and z are non-negative integers such that x < z < y, what is the minimum possible average of x, y, and z?

  1. 10\\frac{1}{3})
  2. 10\\frac{2}{3})
  3. 15
  4. 11
  5. 10

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Explanatory Answer | GRE Averages Practice Question 2

Given Data:

Average of x and y is 15. i.e., \\frac{x + y}{2}) = 15 → x + y = 30

When will the average be minimum?

Because the value of x + y is known, the average of the 3 numbers will be minimum when the value of z is minimized.
But it is given in the question that x < z < y and that these numbers are non-negative integers.
So, if we assign as low a value as possible to x and z, we will have minimized the value of z.
Least possible value for x = 0 and that for z = 1.
Consequently y will be 30 so that the sum x + y = 30

Minimum possible average of x, y, and z = \\frac{0 + 30 + 1}{3}) = \\frac{30}{3}) = 10\\frac{1}{3})

Choice A is the correct answer

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