问一道prep数学题，余数问题

deoxysjjy · 发表于 2011-11-20 16:25:32

154. 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
Answer: C

这道题好纠结啊，求指点

dliu64 · 发表于 2011-11-20 17:14:36

这个题好怪啊。。问题里说到，T is divided by 5, the remainder is 3.. 然后选项2 里又说t is divisible by 5.。。互相矛盾啊！

deoxysjjy · 发表于 2011-11-20 18:11:38

这个题好怪啊。。问题里说到，T is divided by 5, the remainder is 3.. 然后选项2 里又说t is divisible by 5.。。互相矛盾啊！

-- by 会员 dliu64 (2011/11/20 17:14:36)

错了，应该是divisible by 3

qiran19921 · 发表于 2011-11-20 19:20:51

楼主也是今天做prep碰到这题的吗？哇，竟然有这么巧合的事情~~恰好我也问了这题~~~

deoxysjjy · 发表于 2011-11-20 21:25:12

楼主也是今天做prep碰到这题的吗？哇，竟然有这么巧合的事情~~恰好我也问了这题~~~

-- by 会员 qiran19921 (2011/11/20 19:20:51)

然后结果是？

alex318 · 发表于 2011-11-20 21:44:31

n=3x+2, t=5y+3
n*t=15xy+9x+10y+6
if n-2 is divided by 5, n-2=3x can be divided by 5, so 9x=3*3x can be divided by 3*5=15
if t is divided by 3, t-3 can be divided by 3, then t-3=5y can be divided by 3, so y can be divided by 3, so 5y can be divided by 15.
so n*t=15xy+9x+10y+6 is divided by 15, the reminder is 6.

kenny2524289 · 发表于 2011-11-20 22:13:22

1）令n=3a+2,t=5b+3.其中a,b为什么你懂的..
2)使用条件1可以得到3a=5c,使用条件2可以得到5b=3d.这里的c,d也是任意正整数但必须使得等式成立...
这个时候你想一下这个等式怎样可以成立..
3)想完之后就知道可以改写了..条件1:n=15x+2..条件2:t=15y+3...这里的x,y是任意正整数..
4)将条件带入n*t中可以发现..只有两个条件都用了..才可以得到225xy+30y+45x+6..ok....
5)干..可以选了...

deoxysjjy · 发表于 2011-11-20 22:39:18

n=3x+2, t=5y+3
n*t=15xy+9x+10y+6
if n-2 is divided by 5, n-2=3x can be divided by 5, so 9x=3*3x can be divided by 3*5=15
if t is divided by 3, t-3 can be divided by 3, then t-3=5y can be divided by 3, so y can be divided by 3, so 5y can be divided by 15.
so n*t=15xy+9x+10y+6 is divided by 15, the reminder is 6.

-- by 会员 alex318 (2011/11/20 21:44:31)

很牛，了解了

fattybabe · 发表于 2011-11-20 23:12:45

1) u will find out n=15k +2
2) u will find out t=15k+3

combine 1 &2
15k (2+3)/15. so u know the answer.

问一道prep数学题，余数问题

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