Question

In a set of four integer the average of the two smallest integer is102 the average of the three smallest integer is 103 the average of all four is 104 what is the greatest of the integer

Answer 1

Let w, x, y and z be four integers in the increasing order of their values.

Given, average of three smallest integers = 103

⇒ (w + x + y)/3 = 103

⇒ w + x + y = 103×3

⇒w + x + y = 309                                                                                    ...( i )

average of all integers = 104

⇒ (w + x + y + z)/4 = 104

⇒ w + x + y + z = 104×4

⇒w + x + y + z = 416                                                                                       ...( ii )

Subtracting ( i ) form ( ii ),

z = (w + x + y + z) - (w + x + y + z)

= 416 - 309

= 107

The greatest of the four integers is 107.

(As you see above, there is no requirement of the average of the smallest two integers.)