There are 6 consecutive odd numbers. The difference between the square of the average of the first three numbers and the square of the average of the last three numbers is 288. What is the last odd number ?
Let the odd numbers be a , a+2 ,a+4, a+6 ,a+8 and a+10
Average of first 3 odd numbers = (a+2)
Square of Average of first 3 odd numbers = (a+2)$$^2$$
Average of last3 odd numbers = (a+8)
Square of Average of last 3 odd numbers = (a+8)$$^2$$
[(a+8)$$^2$$ ] - [(a+2)$$^2$$ ] =288
a$$^2$$ + 64 + 16a - a$$^2$$ - 4a - 4 = 288
60 + 12a = 288
12a = 228
a= 19
Last odd number = a+10 =29
Hence Option C is the correct answer.
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