Odd One Out: Explanation

The given series of numbers is: 196, 169, 144, 121, 100, 80, 64.

To find the odd one out from this series, we need to identify a number that does not follow the pattern or rule that the other numbers in the series follow.

Pattern in the Series:

- The series is formed by taking the squares of consecutive numbers.
- Each number in the series is the square of the previous number.
- For example, 169 is the square of 13 (13*13), 144 is the square of 12 (12*12), and so on.

Let's analyze each option to determine the odd one out:

a) 169: This number fits the pattern because it is the square of 13.

b) 144: This number also fits the pattern because it is the square of 12.

c) 143: This number is not part of the given series and is not the square of any previous number. It does not follow the pattern.

d) 80: This number fits the pattern because it is the square of 8 (8*8). However, it is also the odd one out because it is the only number in the series that is not a perfect square of a previous number.

Therefore, the correct answer is option 'D' (80) as it does not follow the pattern of the given series.

To summarize:

- The given series of numbers follows a pattern of squaring consecutive numbers.
- Option D (80) is the odd one out as it does not follow the pattern of being a perfect square of a previous number.
- The other options, A (169) and B (144), fit the pattern and are not the odd ones out.
- Option C (143) is not part of the given series and does not follow the pattern.

Answer ( C ) 143