Question

Consider the following 8 numbers, where one labelled x is unknown.

10, 34, 46, x, 26, 41, 26, 16

Given that the range of the numbers is 52, work out 2 values of x

.

Answer 1

Possibilities include -42, 62, -6 or 98

Explanation:

If the range is 52, it must be the difference between the largest and smallest numbers.

The smallest is 10 (or x)

The largest is 46 (or x)

The difference between the two numbers (10 and 46) is 36. Since the range is 52, the missing number, x, must be 10 ± 52 or 46±52.

10 ± 52

-42 or 62

or 46±52

-6 or 98

If the range is 52, then the number x is either -42, 62, -6 or 98.

Answer 2

x = 62 and x = -6

Explanation:

Range = Highest - Lowest

In this case, x can represent either the highest value or the lowest value so let's do both.

Range = Highest - Lowest

x = highest (for the lowest value you take the smallest number among the 8 given)

x - 10 = 52

x = 52 + 10 = 62

Range = highest - lowest

x = lowest (for the highest value, take the the greatest number among the 8 given)

46 - x = 52

- x = 52 - 46 = 6

x = - 6