2009 AMC 8 Problem 11
Attempt Problem 11 of the 2009 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2009 AMC 8 solutions, or check the answer key.
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11.
The Amaco Middle School bookstore sells pencils costing a whole number of cents. Some seventh graders each bought a pencil, paying a total of dollars. Some of the sixth graders each bought a pencil, and they paid a total of dollars. How many more sixth graders than seventh graders bought a pencil?
Answer: D
Small hint:
The pencil price must divide both total costs in cents.
Big hint:
Use the fact that at most sixth graders bought pencils to rule out a -cent price.
Solution:
The number of seventh graders that bought a pencil is divided by the price of a pencil. Similarly, the number of sixth graders that bought a pencil is divided by the price of a pencil.
This means that the price of a pencil divides both and Prime factorizing, we get and The only numbers that divide both and are and
If cent was the price of the pencil, that means sixth graders bought pencils, which is not possible. Therefore, the price of a pencil is cents.
This means that seventh graders bought a pencil, and sixth graders bought a pencil. Therefore, more sixth graders than seventh graders bought pencils.
Thus, D is the correct answer.
Problem 11 in other years
- 1985 AMC 8
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