There are 32 consecutive natural numbers The average of the first 13 numbers is x What is the averag...........

Quantitative Aptitude (MTS) Average

There are 32 consecutive natural numbers. The average of the first 13 numbers is x. What is the average of the next 19

numbers?

This questions was previously asked in

SSC MTS 13th July 2022 Shift-1

X + 15

X + 16

X + 17

X + 18

- Let the first number be n.

- The first 13 numbers: n, n+1, ..., n+12.

- Average of first 13 = (n + n+1 + ... + n+12) / 13 = (13n + 78)/13 = n + 6 = x

- So, x = n + 6

- The next 19 numbers: n+13, n+14, ..., n+31

- Average of these 19 numbers = (n+13 + n+14 + ... + n+31) / 19

- Sum = (n+13) + (n+14) + ... + (n+31) = 19n + (13+14+...+31)

- (13+14+...+31) is arithmetic sum:

- Total numbers = 19, first term = 13, last term = 31

- Sum = 19*(13+31)/2 = 19*22 = 418

- Total sum = 19n + 418

- Average = (19n + 418) / 19 = n + 22

- Recall x = n+6

- New average = x + 16

So the correct option is:

- Option 2: X + 16

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