2004 AMC 12A Problem 3 — Solution | LIVE by Po-Shen Loh

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2004 AMC 12A Problem 3

Below is the professionally curated solution for Problem 3 of the 2004 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 12A solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:Diophantine Equation counting integers in a range

Difficulty rating: 1080

3.

For how many ordered pairs of positive integers $(x, y)$ is $x + 2y = 100?$

$33$

$49$

$50$

$99$

$100$

Solution:

Writing $x = 100 - 2y,$ the value of $x$ is a positive integer precisely when $y$ is a positive integer with $1 \le y \le 49.$

This gives $49$ valid ordered pairs.

Thus, the correct answer is B.

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Problem 3 in Other Years

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