Question

The mean of three numbers is 21. The range of this data set is 12 and the difference between the two smallest numbers
is 3. The greatest of the three numbers is:
​

Answer 1

The greatest of the three numbers is 28

Solution:

Let the three numbers be x, y and z

Where "x" be the smallest number and "z" be the greatest number

According to question,

The mean of three numbers is 21 . Hence we get,

$\frac{x+y+z}{3}=21$

x +y +z = 63  ----- eqn 1

The range of this data set is 12,

Range = highest observation - lowest observation.

Hence we get,

z – x = 12

z = 12 + x  ---- eqn 2

Also, difference between the two smallest numbers is 3

y – x = 3

y = 3 + x ----- eqn 3

Using Equation(2) and (3) in (1) we get,

x + (3 + x) + (12 + x) = 63

3x + 15 = 63

3x = 63 -15

3x = 48

x = 16

Substitute x = 16 in eqn 3,

y = 3 + 16 = 19

Substitute x = 16 in eqn 2,

z = 12 + 16 = 28

Hence the three numbers are 16, 19 and 28

Thus the greatest of three numbers is 28

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