Pls provide the soln for the following with explaination


132) If the integer n is greater than 1, is n equal to 2

1) n has exactly 2 positive factors

2) The difference of any two distinct positive factors of n is odd.


128. If X is an integer is X |X| < 2 x

1)X < 0

2)X=10

Anish,

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-dan

OG 11

Source is OG 11

132.

n>1, is n = 2?
(1) n is prime
Not Sufficient - n could be 2 or any other prime number

(2) The difference of any two distinct positive factors of n is odd.
Sufficient - This is only true of the prime number 2

* If n is a prime other than two, the difference of its two positive factors will be even (1 and itself) --
Odd - Odd = Even

* If n is an even non-prime number, then it will have some difference in factors that are odd (1 and the even number - Even - Odd = Odd), and then it will be divisible by an even number (2 at a minimum) - and the difference between even and even is Even

* if n is an odd non-prime number (15), then it will have some difference in factors that are Even (15 -1); but it will also have two odd factors if it is not prime - given that odd * odd = odd, and Odd - Odd = Even (so B is sufficient)