There are 5 consecutive odd numbers. If the difference between square of the average of first two odd number and the of the average last two odd numbers is 396, what is the smallest odd number?
Solution
Correct Answer: Option A
Let the five consecutive odd numbers be x-4, x-2, x, x+2, x+4
According to the question,
Difference between square of the average of first two odd number and the of the average last
two odd numbers is 396
i.e, x+3 and x-3
\(\begin{array}{l}\Rightarrow\left(\mathrm x\;+\;3\right)^2\;-\;\left(\mathrm x\;-\;3\right)^2\;=\;396\\\Rightarrow\;\mathrm x^2\;+\;9\;+\;6\mathrm x\;-\;\mathrm x^2\;+\;6\mathrm x\;-\;9\;=\;396\\\Rightarrow\;12\mathrm x\;=\;396\\\Rightarrow\;\mathrm x\;=\;33\end{array}\)
Hence, the smallest odd number is 33 - 4 = 29.
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