一道GWD数学题

adasuying2004

Q29:
What is the remainder when the positive integer n is divided by the positive integer k, where k > 1?
(1)      n = (k+1)3
(2)      k = 5
    
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.
Answer: A (GWD:11)

为啥选A？谢谢！！

夏天amy

Q29:
What is the remainder when the positive integer n is divided by the positive integer k, where k > 1?
(1)      n = (k+1)3
(2)      k = 5

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.
Answer: A (GWD:11)

为啥选A？谢谢！！

-- by 会员 adasuying2004 (2011/5/30 1:29:16)

(1)      n = (k+1)3
所以，{ (k+1)* (k+1)* (k+1)}/k Mod 几 也就是 根据乘法的性质三个(k+1)/k 的余数相乘 应该是1
(2)      k = 5
显然不充分 N可以任意取值
哈 不知道讲的清楚不？

我系大P

这样理解吧. 首先1和2一起的话一定可以的. 所以现在重点考虑单单1行不行. 然后n=3k+3, n/k的话就直接余3了. 还是不懂的话就想想, (3k+3)/k=3k/k+3/k, 余数就是3

...写到这里才发现了理解错了, 那个3是次方...那么也同样道理了, (k+1)*(k+1)*(k+1), 其中每个项除以k都余1, 所以最终的余数就是1*1*1就是1了

理解错的那个当做变体吧.....