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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Question : The sum of three consecutive even numbers is 28 more than the average of these three numbers. Then the smallest of these three numbers is:
Option 1: 6
Option 2: 12
Option 3: 14
Option 4: 16
Question : The average of 8 numbers is 18. If one of the numbers is excluded, the average becomes 20. Find the excluded number.
Option 3: 8
Option 4: 4
Question : Three numbers are in the ratio $\frac{4}{5}: \frac{5}{6}: \frac{9}{10}$. The difference between the smallest and the greatest numbers is 12. Find the number which is neither the smallest nor the greatest.
Option 1: 96
Option 2: 108
Option 3: 100
Option 4: 104
Question : The average of three consecutive odd numbers is 52 more than $\frac{1}{3}$rd of the largest number. What is the smallest of these numbers?
Option 1: 79
Option 2: 75
Option 3: 81
Option 4: 77
Question : The average of three consecutive even numbers is A. If the next five even numbers are added, what is the average of these eight numbers?
Option 1: A + 3
Option 2: A + 4
Option 3: A + 5
Option 4: A + 7
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