PP1-203-DS

[pimi]

203. 19582-!-item-!-187;#058&012370
What is the remainder when the positive integer x is divided by 6?

(1) When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0.

(2) When x is divided by 12, the remainder is 3.

Ans: D

我選擇B, 因為題目說x=6a+r, (2)說x=12b+3, 可以把(2)整理成6(2b)+3, 就可以得到餘數是3

但是為何A也可以解出答案呢？？？

[amazingslim]

203. 19582-!-item-!-187;#058&012370
What is the remainder when the positive integer x is divided by 6?

(1) When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0.

(2) When x is divided by 12, the remainder is 3.

Ans: D

我選擇B, 因為題目說x=6a+r, (2)說x=12b+3, 可以把(2)整理成6(2b)+3, 就可以得到餘數是3

但是為何A也可以解出答案呢？？？

之前看過大陸人提供這種問題的算法
(1)設x=2a+1=3b
找數字代進去公式相等,a.b最小均為1,so x=3(也就是說餘數為3)
當a=4,b=3,x=9(但是被6除，餘數還是3)
所以x=6c+3(6為2跟3最小公倍數)

[pimi]

感激大大回覆

想請問設x=2a+1=3b, 再代數字, 感覺不是很保險, 畢竟考試也沒有太多時間讓我們帶太多數字, 而代的數字樣本數不夠, 又擔心會有啥例外出現 > <

像B選項很明顯, 不需要透過帶數字, 就可以看出答案, 但A~~~~
哀哀
請大大指導～

[scottkidd]

題目要知道x除以6的餘數...
(1) When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0.

6=2*3
可以知道若x被6整除，則需要x同時是2和3的倍數
但(1)說x是3的倍數，但是x被2除卻餘1(這可以推x是奇數)，
這樣有兩個方向可以想：
(a)被3整除，除2卻餘1，可以推得餘數一定是2+1=3
OR (b)直接找是3的倍數同時是奇數的代看看就可以知道了