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(x^{2} + 105)

⇒ x^{2} + 6x + 9 = x^{2} + 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**