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In an auditorium,360 chairs are to be set up in a rectangular arrangement with X rows of exactly Y chairs each.If the only other
In an auditorium,360 chairs are to be set up in a rectangular arrangement with X rows of exactly Y chairs each.If the only other
admin
2022-10-18
42
问题
In an auditorium,360 chairs are to be set up in a rectangular arrangement with X rows of exactly Y chairs each.If the only other restriction is that 10<x<25. how many different rectangular arrangements are possible?
选项
A、Four
B、Five
C、Six
D、Eight
E、Nine
答案
B
解析
Because a total of 360 chairs are distributed in x rows of exactly y chairs each, it follows that xy = 360. Also, 10 < x < 25, and so x can only be an integer factor of 360 = 2
3
× 3
2
× 5 that is between 10 and 25. Below is a list of all integers from 11 through 24. Since 2,3, and 5 are the only prime factors of 360, any integer having a prime factor other than 2,3, or 5 cannot be a factor of 360 and has been crossed out. For example, 21 = 3×7 has a prime factor of 7, and thus 21 has been crossed out.
Of the six integers remaining, it is clear that each is a factor of 360 = 2
3
× 3
2
× 5 except for 16 = 2
4
. Therefore, the number of possible rectangular arrangements is five.
The correct answer is B.
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