sanjoo wrote:
If x is an integer and |1−x|<2 then which of the following must be true?
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
If x is an integer and |1-x|<2 then which of the following must be true?|1-x| is just the distance between 1 and x on the number line. We are told that this distance is less than 2: --(-1)
----1----3-- so, -1<x<3. Since given that x is an integer then
x can be 0, 1 or 2.
A. x is not a prime number. Not true if x=2.
B. x^2+x is not a prime number. Not true if x=1.
C. x is positive. Not true if x=0.
D. Number of distinct positive factors of x+2 is a prime number. True for all three values of x.
E. x is not a multiple of an odd prime number. Not true if x=0, since zeo is a multiple of every integer except zero itself.
Answer: D.
Thank you for the explanation. May you please elaborate why zero cannot be a multiple of itself?