2008 AMC 10B Problem 1

Attempt Problem 1 of the 2008 AMC 10B 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 2008 AMC 10B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

A basketball player made $5$ baskets during a game. Each basket was worth either $2$ or $3$ points. How many different numbers could represent the total points scored by the player?

$2$

$3$

$4$

$5$

$6$

Answer: E

Concepts:basic counting systematic listing

Difficulty rating: 720

Solution:

If $k$ of the baskets are worth $3$ points and the rest worth $2,$ the total is $2(5-k)+3k=10+k.$

As $k$ ranges over $0,1,\ldots,5,$ the total takes every integer value from $10$ to $15,$ giving $6$ possibilities.

Thus, the correct answer is E.

Full Exam

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