[求助] 弱问一道余数DS题

aprilavrilx

做prep08，碰到这个题，一直想不出解法，看到版上说是余数题，但没怎么看懂，请高手点拨一下吧，不甚感激！

If N is an integer and R is the reminder 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.

stevehong

选A

stevehong

1) n not divisible by 2=> n is odd=> (n-1) and (n+1) must be consective even numbers.

if n=1, 0*2/24 leaves remainder 0
if n=3, 2*4/24 leaves remainder 8
not sufficient


2) n not divisible by 3=> n can be even or 1, 5, 7, 11, 13....

if n=5, 4*6/24 leaves remainder 0
if n=2, 1*3/24 leaves remainder 3
not sufficient

together,
n must be odd and not divisible by 3=> n can be 1, 5, 7, 11, 13...
if n=7, 6*8/24 leaves remainder 0
if n=11, 10*12/24 leaves remainder 0

hence C.

aprilavrilx

楼上stevehong大侠正解，prep里答案是C，懂了，非常感谢！