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 1: A + 1
Option 2: A – 2
Option 3: A + 2
Option 4: A + 3
Correct Answer: A + 1
Solution :
7 consecutive odd numbers as $x, x+2,x+4, x+6,x+8, x+10, x+12$.
So, A = $x+6$ (Midterm is the average)
Since the average of 7 consecutive odd numbers is A, so the sum of these numbers is 7A
⇒ The next 3 odd numbers are $x +14,x +16, x +18$ and previous 2 odd numbers are $x-2 , x-4$
⇒ New Average = $\frac{((x-2)+(x-4)+x+(x+2)+(x+4)+(x+6)+(x+8)+(x+10)+(x+12)+(x+14)+(x+16)+(x+18))}{12}$
= $\frac{12x +84}{12}$
= $x + 7$
= A +1
Hence, the correct answer is A +1.
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