While listing N consecutive even numbers for determining their average the last number by mistake go...........

Quantitative Aptitude (MTS) Average

While listing N consecutive even numbers for determining their average, the last number, by mistake, got replaced by the next

odd number and thereby the average turned out to be more than the desired value by 0.0125. What is the value of N?

This questions was previously asked in

SSC MTS 18th October 2021 Shift-3

100

- Let's consider N consecutive even numbers starting with 2k. So, the numbers are 2k, 2k+2, ..., 2k+2(N-1).

- The average of these N numbers is \( \frac{2k \cdot N + N(N-1)}{N} = 2k + N - 1 \).

- If the last number becomes the next odd number instead of an even number (2k+2N-1), the sum becomes 1 more than the original.

- The average will now be \( 2k + N - 1 + \frac{1}{N} \).

- New average - original average = 0.0125.

- \(\frac{1}{N} = 0.0125\).

- Solving gives \( N = 80 \).

- Option 1: 80 is the correct answer.

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