GWD-4-15 数学 请教

doudou8

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.

                                                                                                                              

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

windygirl

C                          

dominique11

Windgirl, could you let me know why C?

windygirl

1,n is odd

(n-1)(n+1)/24=M*(M+1)/6=A/3

the remainder is unsure.

2,(n-1)(n+1)/6=[3X(3x+2)or3(3x+1)(X+1)]/24=Q/8 the remainder is unsure

1+2n-1)(n+1)can be divided by 3.

3 is a factor of A

企企

选C

根据(1) 2不是factor,那么举例3，5，r分别为8,0,所以不行

根据（2），3不是factor,那么举例2，4， r分别为3，15,所以不行

但是如果1,2一起，那么n可以表示为6x+1 or 6x＋5

then, （n+1)(n-1)=6x(6X+2)所以能被24整除，r=0

     or (n+1)（n－1）＝(6x+4)(6x+6)也能被24整除，r也为0

所以此题选C