2. 外语
  3. 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

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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 = 23 × 32 × 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 = 23 × 32 × 5 except for 16 = 24. Therefore, the number of possible rectangular arrangements is five.
The correct answer is B.
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