2021 AMC 12A Fall Problem 2

Below is the professionally curated solution for Problem 2 of the 2021 AMC 12A Fall, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 12A Fall solutions, or check the answer key.

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Concepts:rectangle area

Difficulty rating: 1020

Menkara has a $4 \times 6$ index card. If she shortens the length of one side of this card by $1$ inch, the card would have area $18$ square inches. What would the area of the card be in square inches if instead she shortens the length of the other side by $1$ inch?

$16$

$17$

$18$

$19$

$20$

Solution:

The original card is $4 \times 6.$ Shortening a side by $1$ inch gives area $18,$ which requires $3 \times 6 = 18,$ so the reduced side was the $4$ -inch side.

Shortening the other side by $1$ inch instead gives $4 \times 5 = 20$ square inches.

Thus, the correct answer is E.

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