pp-T1-DS123

[Huang Hsin-Yi]

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
有點金剛摸不著二丈

[FIG]

n=3x+2
t=5y+3

nt=15xy+10y+9x+6

n - 2 is divisible by 5.
=>n-2=(3x+2)-2=3x is divisible by 5.
=>x is divisible by 5

t is divisible by 3.
t=5y+3 =>y is divisible by 3.

so nt=15xy+10y+9x+6
15xy is divisible by 15
10y is divisible by 15
9x is is divisible by 15
the remainder is 6

[Huang Hsin-Yi]

謝謝你,終於恍然大悟