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If the average of 6 consecutive even number is 25, the difference between the largest and the smallest number is :

A. 8 B. 10 C. 12 D. 14 Answer: Option B
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Solution(By Apex Team)

According to the question, Sum of 6 consecutive even number is = 25 × 6 = 150 $\begin{array}{l}Sn=\frac{n}{2}[2a+(n-1)\times d]\\ \Rightarrow150=\frac{6}{2}[2a+(6-1)\times2]\\ \Rightarrow150=\frac{6}{2}(2a+10)\\ \Rightarrow300=12a+60\\ \Rightarrow12a=240\\ \Rightarrow a=\frac{240}{12}\\ \Rightarrow a=20\end{array}$ ∴ Numbers are 20, 22, 24, 26, 28, 30 Difference between largest and smallest is = 30 – 20 = 10 Alternate : Let the 6 consecutive number is = x, x + 2, x + 4, x + 6, x + 8, x + 10 According to the question, Largest number = Average + (n – 1) = 25 + 5 = 30 Smallest number = Average – (n – 1) = 25 – 5 = 20 Difference between largest and smallest number = 30 – 20 = 10

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