Correct option is C
Given:
- Four consecutive even numbers.
- The difference between the squares of the averages of the first two and the last two numbers is 408.
Formula Used:
- Let the four consecutive even numbers be: x, x+2, x+4, x+6
- Average of first two numbers = 2(x+x+2)=x+1
- Average of last two numbers = 2(x+4+x+6)=x+5
- Difference of squares = (x+5)2−(x+1)2=408
Solution:
Let the numbers be x, x+2, x+4, x+6
Then, average of first two = x + 1
And, average of last two = x + 5
(x+5)2−(x+1)2=408 =>[x2+10x+25]−[x2+2x+1]=408 =>x2+10x+25−x2−2x−1=408 =>8x+24=408 =>8x=384 =>x=48
Largest number = x + 6 = 48 + 6 = 54
The largest even number is 54.