When 15 is included in a list of natural numbers their…

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When 15 is included in a list of natural numbers, their mean is increased by 2. When 1 is included in this new list, the mean of the numbers in the new list is decreased by 1. How many numbers were there in the original list?

  1. A. 4
  2. B. 5
  3. C. 6
  4. D. 8

Answer: Option A

Here is complete explanation of When 15 is included in a list of natural numbers their….

Solution(By ExamCraze Team)

Let there be n numbers in the original list and let their mean be x.
Then, sum of n numbers = nx
$$eqalign{ & therefore frac{{nx + 15}}{{n + 1}} = x + 2 cr & Rightarrow nx + 15 = left( {n + 1} right)left( {x + 2} right) cr & Rightarrow nx + 15 = nx + 2n + x + 2 cr & Rightarrow 2n + x = 13.....(i) cr} $$
And,
$$eqalign{ & therefore frac{{nx + 16}}{{n + 2}} = left( {x + 2} right) - 1 cr & Rightarrow nx + 16 = left( {n + 2} right)left( {x + 1} right) cr & Rightarrow nx + 16 = nx + n + 2x + 2 cr & Rightarrow n + 2x = 14.....(ii) cr} $$
Solving (i) and (ii), we get:
n = 4, x = 5

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