AMC12 2010 B

AMC12 2010 B · Q3

AMC12 2010 B · Q3. It mainly tests GCD & LCM.

A ticket to a school play cost $x$ 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 $\$48$，一群 10 年级学生买票总共花费 $\$64$。$x$ 有多少可能的值？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (E)

正确答案：（E）

Solution

We find the greatest common factor of $48$ and $64$ to be $16$. The number of factors of $16$ is $5$ which is the answer $(E)$.

$48$ 和 $64$ 的最大公因数是 $16$。$16$ 的因数个数是 $5$，因此答案是 $(E)$。

Topics

NT.003 GCD & LCM