If x is an integer and |1-x|<2 then which of the following must be true?	Choose the correct choice from the following choices: A) x is not a prime number B) x^2+x is not a prime number C) x is positive D) Number of distinct positive factors of x+2 is a prime number E) x is not a multiple of an odd prime number
1−x|&lt;2 = -2&lt;(1-x)&lt;2   = -3&lt;-x&lt;1   = 3&gt;x&gt;-1   So x can hold values of 0,1 &amp; 2 to satisfy the condition. Now we can evaluate the choices.   A) 1 &amp; 2 primes, so incorrect   B) 1^2+1=2 is a prime, so incorrect   C) 0 is not +ve, So incorrect   D) x+2= 2,3,or 4, here 2 has 2 factor(prime), 3 has 2 factor (prime) &amp; 4 has 3 factors (prime). Hence correct choice.   E) 2 is multiple of 1. So incorrect.   Hence Answer Number of distinct positive factors of x+2 is a prime number.
<result>D</result>
If x is an integer and |1-x|<2 then which of the following must be true?