2021 AMC 12A Fall Problem 2

Question

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

Shortening a side by

1

to get area

18

means

3 \times 6 = 18,

so the

4

-inch side was the one reduced

Instead reduce the

6

-inch side by

1,

giving

4 \times 5

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.

Problem 2 in other years