AMC10 2010 B
AMC10 2010 B · Q8
AMC10 2010 B · Q8. It mainly tests GCD & LCM.
A ticket to a school play costs $x$ dollars, where $x$ is a whole number. A group of 9th graders buys tickets costing a total of \$48, and a group of 10th graders buys tickets costing a total of \$64. How many values for $x$ are possible?
学校戏剧的门票价格为 $x$ 美元，其中 $x$ 是整数。一群 9 年级学生买票总共花费 48 美元，一群 10 年级学生买票总共花费 64 美元。$x$ 可能取的值有多少个？
(A)
1
1
(B)
2
2
(C)
3
3
(D)
4
4
(E)
5
5
Answer
Correct choice: (E)
正确答案：（E）
Solution
The cost of an individual ticket must divide 48 and 64. The common factors of 48 and 64 are 1, 2, 4, 8, and 16. Each of these may be the cost of one ticket, so there are 5 possible values for $x$.
单张票价必须能整除 48 和 64。48 和 64 的公因数是 1、2、4、8 和 16。这些都可以作为单张票价，所以 $x$ 有 5 个可能值。
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