AMC 8 2012 Problem 13
AMC8 2012 年第 13 题
整除与因数★★★☆☆
Jamar bought some pencils costing more than a penny each at the school bookstore and paid $1.43 . Sharona bought some of the same pencils and paid $1.87 . How many more pencils did Sharona buy than Jamar?
Jamar 在学校的书店买了一些铅笔，每支价格超过 1 美分，总共付了 1.43 美元。Sharona 也买了一些相同的铅笔，总共支付 1.87 美元。那么 Sharona 买的铅笔教比 Jamar 多多少支？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
We assume that the price of the pencils remains constant. Convert $1.43 and $1.87 to cents. Since the price of the pencils is more than one penny, we can find the price of one pencil (in cents) by taking the greatest common divisor of 143 and 187, which is 11. Therefore, Jamar bought pencils and Sharona bought pencils. Thus, Sharona bought 17-13 = 4 more pencils than Jamar.
We find the difference between 1.43 and 1.87 is 1.87-1.43 = 0.44, which is the extra cost of Sharona's pencils over Jamar's pencils. Because the difference between the numbers of pencils they bought must divide 0.44 evenly, looking into the answers, 2 or 4 is possibly correct. It gives the price of each pencil as or , respectively. Then we find only 0.11 can divide 1.43 and 1.87 evenly. So the answer is 4. You can quickly tell, if you have memorized the multiplication table, that 187 and 143 are both multiples of 11 (also their GCF). Additionally, the difference is 44 cents, which means there are 4 more pencils purchased by Sharona because 11×4 = 44.
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