Correct Answer - Option 4 : 72
Given:
Square of average of last 3 numbers = 420 more than the square of smallest number of the set
Formula used:
Average = Sum of Observations/Total number of Observations
Calculation:
Let the 5 consecutive even numbers be 2x , 2x + 2, 2x + 4, 2x + 6, 2x + 8 respectively
Now, according to question
⇒ [(2x + 4 + 2x + 6 + 2x + 8)/3]2 = 420 + (2x)2
⇒ [(6x + 18)/3]2 = 420 + (2x)2
⇒ 36(x + 3)2/9 = 4(x2 + 105)
⇒ x2 + 6x + 9 = x2 + 105
⇒ 6x = 96
⇒ x = 16
Now, the smallest number = 2x
⇒ 2 × 16 = 32
And the Largest number = 2x + 8
⇒ 2 × 16 + 8 = 40
Now, the sum of smallest and largest even number together = 32 + 40
⇒ 72
∴ Required sum is 72