2021 AMC 10A Fall Problem 2

Below is the professionally curated solution for Problem 2 of the 2021 AMC 10A Fall, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 10A Fall solutions, or check the answer key.

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Concepts:rectangle area work backwards

Difficulty rating: 560

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:

If she shortens the $4$ -inch side by $1$ , she has a $3\times 6$ card, whose area is $18$ square inches.

Therefore the given shortening was on the $4$ -inch side. Shortening the other side instead gives a $4\times 5$ card, with area $20$ square inches.

Thus, E is the correct answer.

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