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A set has 5 consecutive even numbers. Square of average of last 3 numbers of the set is 420 more than the square of smallest number of the set. What is the sum of smallest and largest even numbers of the set together.
1. 74
2. 76
3. 70
4. 72
5. 78

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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

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