[問題]天山 04-28

[tandy]

A school administrator will assign each student in a group of n students to one of m clasrooms. If 3<m<13<n, is it possible to assign each of the n students to one of the m classrooms fo that each classroom has the same number of students assigned to it?
(1)it is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it
(2)it is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it答案是B請問是為什麼呢?我連題目都看不太懂><

[zazer.lin]

A school administrator will assign each student in a group of n students to one of m clasrooms. If 3<m<13<n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
(1)it is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it
(2)it is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it
答案是B

題目大至上是說要將n個學生塞進m間教室(3<m<13<n)...問是否每間教室的人數可能一樣..
換言之...就是問n能不能被m整除

statement(1) 將3n的學生塞進m間教室...使得每間教室人數一樣
但要注意的是...3<m<13...這會有兩種情形:
<i> m是3的倍數...但n並不是3的倍數
ex: if m = 6 and n = 20, then 3n = 60 =10 * 6 = 10m
但 n=20 並不能被 m=6 整除
<ii> m是3的倍數...且n也是3的倍數
ex: if m = 6 and n = 18, then 3n = 54 = 6 * 9 = 9m
且 n=18 可以被 m=6 整除
by <i><ii>可得知...statement(1)不充分

statement(2) 將13n的學生塞進m間教室...使得每間教室人數一樣
這就沒問題了...因為3<m<13...所以 n 一定是 m的倍數

小弟的文字敘述能力不是很好:PP...希望你能看得懂...

[tsaowen]

A school administrator will assign each student in a group of n students to one of m clasrooms. If 3<m<13<n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
(1)it is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it
(2)it is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it
答案是B

題目大至上是說要將n個學生塞進m間教室(3<m<13<n)...問是否每間教室的人數可能一樣..
換言之...就是問n能不能被m整除

statement(1) 將3n的學生塞進m間教室...使得每間教室人數一樣
但要注意的是...3<m<13...這會有兩種情形:
<i> m是3的倍數...但n並不是3的倍數
ex: if m = 6 and n = 20, then 3n = 60 =10 * 6 = 10m
但 n=20 並不能被 m=6 整除
<ii> m是3的倍數...且n也是3的倍數
ex: if m = 6 and n = 18, then 3n = 54 = 6 * 9 = 9m
且 n=18 可以被 m=6 整除
by <i><ii>可得知...statement(1)不充分

statement(2) 將13n的學生塞進m間教室...使得每間教室人數一樣
這就沒問題了...因為3<m<13...所以 n 一定是 m的倍數

小弟的文字敘述能力不是很好:PP...希望你能看得懂...

解的真仔細
謝謝~~

[tandy]

了解了解,
zazer.lin真的解釋的非常仔細呢!!
謝謝喔!!!