Question : If the average of 6 consecutive even numbers is 25, the difference between the largest and the smallest number is:
Option 1: 8
Option 2: 10
Option 3: 12
Option 4: 14
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Correct Answer: 10
Solution :
Let $(x–5),(x–3),(x–1),(x+1), (x+3)$ and $(x+5)$ be the 6 consecutive even numbers.
Average of 6 consecutive even numbers = Average of two middle terms
$25 = \frac{(x–1)+(x+1)}{2}$
⇒ $x = 25$
Difference between the largest and the smallest number = $(x+5)–(x–5) = 30 – 20 = 10$
Hence, the correct answer is 10.
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