P2-DS-123

[vantreal]

123. 12975-!-item-!-187;#058&009772
When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15 ?

(1) n - 2 is divisible by 5.

(2) t is divisible by 3.

Ans: (C)

請各位大大解說吧, 謝謝.
還有請問遇到這種要求remainder的題目, 只能靠帶數字進去嗎?

[cktseng]

123. 12975-!-item-!-187;#058&009772
When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15 ?

(1) n - 2 is divisible by 5.

(2) t is divisible by 3.

Ans: (C)

===================================

n=3x+2
t=5y+3
nt =15xy+10y+9x+6

1. n-2 = 5a => 3x+2-2 = 5a => 3x is divisible by 5 => n=15b+2
2. t = 5c => 5y is divisible by 3 => t=15d+3

From 1 & 2, => nt = 15Z + 6
Answer = C

[vantreal]

big thx :)