Question 10

The average of 8 consecutive integers is 23/2. What is the average of first three integers?

Solution

Let the 8 consecutive integers be = $$(x),$$ $$(x+1),$$ $$(x+2),$$ $$(x+3),$$ $$(x+4),$$ $$(x+5),$$ $$(x+6)$$ and $$(x+7)$$

Sum of integers = $$(x)+$$ $$(x+1)+$$ $$(x+2)+$$ $$(x+3)+$$ $$(x+4)+$$ $$(x+5)+$$ $$(x+6)+(x+7)$$ $$=\frac{23}{2}\times8$$

=> $$8x+28=92$$

=> $$8x=92-28=64$$

=> $$x=\frac{64}{8}=8$$

$$\therefore$$ Average of first three integers = $$\frac{(8)+(8+1)+(8+2)}{3}$$

= $$\frac{27}{3}=9$$

=> Ans - (A)


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