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
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Correct Answer: 77
Solution : Let $(x–2), x$ and $(x+2)$ be the 3 consecutive odd numbers. Average of AP with an odd number of terms = middle term ⇒ Average = $x$ Since the average of 3 consecutive odd numbers is 52 more than $\frac{1}{3}$rd of the largest number, $x = 52+\frac{(x+2)}{3}$ ⇒ $3x = (52×3)+(x+2)$ ⇒ $2x = 158$ ⇒ $x = 79$ Smallest number = 79 – 2 = 77 Hence, the correct answer is 77.
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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 seven consecutive numbers is 20. The largest of these numbers is:
Option 1: 24
Option 2: 23
Option 3: 22
Option 4: 20
Question : The sum of three fractions is $2\frac{11}{24}$. On dividing the largest faction by the smallest fraction, $\frac{7}{6}$ is obtained which is $\frac{1}{3}$ greater than the middle fraction. The smallest fraction is:
Option 1: $\frac{5}{8}$
Option 2: $\frac{3}{4}$
Option 3: $\frac{5}{6}$
Option 4: $\frac{3}{7}$
Question : The average of four consecutive odd numbers is 40. What is the largest number?
Option 1: 42
Option 2: 45
Option 3: 43
Option 4: 44
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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