[求助]TT3-16

Q16:

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)     2 is not a factor of n.

(2)     3 is not a factor of n.

答案是C

Let me try:

Stem1:
n is not divisible by 2 means n is odd
so,

(n-1) is even and
(n+1) is even
And n could be 3,5,7,9,
so,
(3-1)*(3+1)/24 = remainder=8
(5-1) *(5+1)/24 = remainder=0
(7-1)*(7+1)/24 = remainder=0
(9-1)*(9+1)/24 = remainder=8
so, r could be 0 or 8 NOT SUFF.
Stem2:

n is not divisible by 3
so, n could be 1,2,4,5,7,8,10,11,13,14,16,17 & so on

0/24 = remainder=0
(2-1)*(2+1)/24 = rem=3
(4-1)*(4+1)/24 = rem=9. NOT SUFF.

Combining both:

n could be 1,3,5,7,9,11,13,& so on(from 1)
n could be 1,2,4,5,7,8,10,11,13,14,16,17 & so on
so, n could only be odd & not divisible by 3 so,

n could be 1,5,7,11,13,17,19,23
so, (n-1)*(n+1)/24 will always give remainder 0. SUFF.

Hence, answer is C.

多谢