Question

The arithmetic mean of the four different natural numbers is 110. If the largest of these four numbers is 135, then what is the maximum possible value of the range of the set of these four numbers?
1. 97
2. 96
3. 98
4. 95

Answer 1

Correct Answer - Option 1 : 97

Given:

mean of four numbers = 110

largest number = 135

Formula used:

Mean = Sum of observations/Number of observation

Range of set = largest number – smallest number

Calculation:

Sum of all numbers = 440

Sum of numbers other than the largest = 440 – 135 = 305

for the value of the range to be maximum other two numbers should be 134 and 133 as all numbers are different.

Smallest number = 305 – (134 + 133) = 38

Range = 135 – 38 = 97

∴ The range of the set of these four numbers is 97