Odd Man Out in a Given Series

Introduction
In this question, we are given a series of numbers: 835,734,642,751,853,981,532. We need to identify the odd man out from this series and explain the reason behind it.

Solution
The given series of numbers can be analyzed in different ways to identify the odd man out. Here are some possible methods:

1. Prime Numbers: We can check whether the given numbers are prime or composite. The odd man out will be the number that is either prime or composite while the rest of the numbers are of the opposite type.

- 835 = composite (5 x 167)
- 734 = composite (2 x 367)
- 642 = composite (2 x 3 x 107)
- 751 = prime
- 853 = prime
- 981 = composite (3 x 327)
- 532 = composite (2 x 2 x 7 x 19)

Therefore, the odd man out is 751 because it is the only prime number in the series.

2. Patterns: We can look for any pattern in the given numbers and identify the one that does not fit the pattern.

- 835 - 734 = 101
- 734 - 642 = 92
- 642 + 109 = 751
- 751 + 102 = 853
- 853 + 128 = 981
- 981 - 449 = 532

The pattern seems to be alternating subtraction and addition of consecutive numbers, except for the fourth and fifth numbers which are primes. Therefore, the odd man out is 751 because it does not fit the pattern.

Conclusion
Based on the above analysis, we can conclude that the odd man out in the given series of numbers 835,734,642,751,853,981,532 is 751 because it is the only prime number in the series and does not fit the pattern of alternating addition and subtraction of consecutive numbers.