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The average of five consecutive numbers is x. If the next two numbers are included, how shall the average vary?
- A. It shall increase by 1
- B. It shall remain the same
- C. It shall increase by 1.4
- D. It shall increase by 2
Answer: Option A
Here is complete explanation of The average of five consecutive numbers is x If the next….
Solution(By ExamCraze Team)
Let the five consecutive numbers be z, z + 1, z + 3 and z + 4
Then,
$$ Rightarrow frac{{z + left( {z + 1} right) + left( {z + 2} right) + left( {z + 3} right) + left( {z + 4} right)}}{5} = x$$
$$eqalign{
& Rightarrow 5z + 10 = 5x cr
& Rightarrow z = frac{{5x - 10}}{5} cr
& Rightarrow z = x - 2 cr} $$
So, the numbers are x - 2, x - 1, x, x + 1, x + 2
∴ Required mean
$$ = frac{{left( {x - 2} right) + left( {x - 1} right) + x + left( {x + 1} right) + left( {x + 2} right) + left( {x + 3} right) + left( {x + 4} right)}}{7}$$
$$eqalign{
& = frac{{7x + 7}}{7} cr
& = x + 1 cr} $$
