Statement 1: The sum of all positive factors of 'n' that are less than 'n' is equal to 'n'.
A perfect number is a positive integer that is equal to the sum of its positive factors.
Examples are 6, 28, 478, etc.
This statement implies that n = positive numbers = 6, 28, 478, ...
However, the information provided is not enough to arrive at a definite value in the range of perfect numbers.
Hence, statement 1 is NOT SUFFICIENT.
Statement 2: n < 30
This means that 0 < n < 30. 'n' can be any number within the range of positive integers between 1 and 30. e.g 1, 2, 3, ..., 29.
However, the information provided is not enough to arrive at a definite answer; hence, statement 2 also is NOT SUFFICIENT.
Combining both statements together:
Statement 1: n is a perfect number
Statement 2: n < 30
Therefore, 'n' is a perfect number that is less than 30 which means 'n' can either be equal to 6 or 28.
Since the exact value of 'n' remains unknown, then both statements combined together are NOT SUFFICIENT.
Therefore, the correct answer is option E.
Thanks.
