Bunuel wrote:
Official Solution:
If \(x\) is an integer and \(|1-x| \lt 2\) 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
\(|1-x|\) 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, \(-1 \lt x \lt 3\). Since it is 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 zero is a multiple of every integer except zero itself.
Answer: D
Hello Bunuel
In E, why did you say that "zero is a multiple of every integer
except zero itself."? Isn't 0 a multiple of 0 itselft?