Question : The average of seven consecutive even numbers is 12. What will be the new average if the next even number is also considered?
Option 1: 16
Option 2: 13
Option 3: 14
Option 4: 15
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Correct Answer: 13
Solution : The average of seven consecutive even numbers = 12 The sum of seven consecutive even numbers = 12 × 7 = 84 Let $x$ be the first number So, $x + (x+2) + (x+4) + (x+6) +(x+8) + (x+10) + (x+12)$ = 84 ⇒ $7x+ 42 = 84$ ⇒ $x = \frac{84-42}{7} = 6$ New number added = $x+14 = 6+14 = 20$ When 20 is added, Sum = 84 + 20 = 104 So, the average = $\frac{104}{8}$ = 13 Hence, the correct answer is 13.
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Question : There are 32 consecutive natural numbers. The average of the first 13 numbers is $x$. What is the average of the next 19 numbers?
Option 1: $x+15$
Option 2: $x+16$
Option 3: $x+17$
Option 4: $x+18$
Question : The average of 5 consecutive numbers is A. If the next 3 numbers are also taken, what will be the new average?
Option 1: A + 1
Option 2: A + 1.5
Option 3: A + 2
Option 4: A + 2.5
Question : The average of 7 consecutive odd numbers is A. If the next 3 and the previous 2 odd numbers to these 7 odd numbers are also included, what is the new average of these 12 consecutive odd numbers?
Option 2: A – 2
Option 4: A + 3
Question : The average of five consecutive odd numbers is 15. What is the smallest of these five numbers?
Option 1: 11
Option 3: 15
Option 4: 9
Question : The average of 11 numbers is 8. If every number is tripled, then what will be the new average of the numbers?
Option 1: 8
Option 2: 24
Option 3: 16
Option 4: 32
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