求教PREP里面几道数论的题

musicbbt

(1)X是正整数，x,6,9的最小公倍数？

 （1）x和6的最小公倍数是30
 （2）x和9的最小公倍数是45

答案：D  

 

If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?

(1) n is not divisible by 2.

(2) n is not divisible by 3.

答案：C

第一个一看就知道选D，第二个代入法也没问题，有没有公式或者推导过程，总觉得带入不是很严谨

 

If x, y, and z are integers and xy + z is an odd integer, is x an even integer?

(1) xy + xz is an even integer.

(2) y + xz is an odd integer.

这个答案是A,我绕来绕去，完全没思路，请NN帮助解答一下，谢谢！