[問題]GWD 5-11

[michelle610]

Q11:
If x is a positive integer, is the remainder 0 when 3[sup]x[/sup]+1 is divided by 10?
(1)x = 4n + 2, where n is a positive integer
(2) x > 4

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.

the Answer is A but why 我不懂這题的思路ㄟ
請好心人幫忙一下嚕 我在彙整那裡也找不到這题[sup][/sup]

[becker]

3[sup]x[/sup]+1 要被10整除，所以3[sup]x[/sup]的各位是一定是9，
3[sup]1[/sup]= 3
3[sup]2[/sup]= 9
3[sup]3[/sup]=27
3[sup]4[/sup]=81
3[sup]5[/sup]=243
3[sup]6[/sup]=729
.
.
.
它個位數是以 3. 9. 7. 1在循環，
所以x在 2 6 10....的時候，3[sup]x[/sup]的個位數都是9,加1就被乘10的倍數了
當然就被整除，
條件二就不用看了。

[michelle610]

真是謝謝becker的解說囉 清楚明確

[VC]

計算此題時把A選項代入
x=4n+2
n=1代入
x=6
則得729+1=800
所以A答案OK
B選項以x=5代入
答案不合，故錯誤