PP-T1-DS-157

[拎]

157. 15663-!-item-!-187;#058&010465
If n is a positive integer and r is the remainder when 4 + 7n is divided by 3, what is the value of r ?

(1) n + 1 is divisible by 3.

(2) n > 20

ANS: (A)

常常搞不懂餘數的題目~請問有哪位大大可以教一下呢?? 謝謝

[chiungfen]

首先，4 + 7n is divided by 3 SO 餘數一定是0。
(1) n + 1 is divisible by 3. 同樣被3整除，
所以餘數一定也是0............sufficient

(2) n > 20, 代入4 + 7n的話，餘數就有很多種不一樣的答案，
如:代21、22就知了，兩個的餘數不一樣，so無法得知一個確切的r囉~~~

[拎]

可是題目是說 "r is the remainder when 4 + 7n is divided by 3", 並沒有說 4+7n 是被3整除的....

[chiungfen]

n=2,3, 4, 5, 6, 7, .........代入4 + 7n 及n+1 餘數都會一樣的。n=某數，而4 + 7n 及n+1 餘數一樣
那就是value of r 了

[Weichieh]

(1) n + 1 is divisible by 3
設 n+1 = 3a, n = 3a-1,
原式：4 + 7n
= 4+7(3a-1) = 21a -3
題幹說r 是21a-3除以3的餘數，
因為21a-3被3整除，所以r=0