400-1816-180
本題由chris提供
A school administrator will assign each student in a group
(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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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文字解析
某個(gè)學(xué)校
條件一：如果安排3n個(gè)學(xué)生到m個(gè)教室，那么可以做到每個(gè)教室里的人數(shù)都一樣。
條件二：如果安排13n個(gè)學(xué)生到m個(gè)教室，那么可以做到每個(gè)教室里的人數(shù)都一樣。
解析：
條件一說明3n能夠被m整除，那么m可能值有4,5,6,7,8,9,10,11,12，其中6,9,12均是3的倍數(shù)，3n/m可約分，導(dǎo)致3n/m的整除與n/m的整除之間沒有必然聯(lián)系。例如，m=6，n=16，3n/m=8，但是n/m=8/3，不能整除，所以（1）不充分；
條件二說明13n能夠被m整除，那么m可能值有4,5,6,7,8,9,10,11,12，沒有13這個(gè)因子，且13是質(zhì)數(shù)，所以13n/m無論m為何值均不能將13約分下去，這就導(dǎo)致了若想13n/m是整數(shù)，則n/m必須是整數(shù)。所以（2）充分。
選B
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