2021 AMC 10A 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

Figure out which side was shortened to get area

18

Then shorten the other side instead

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.

Problem 2 in other years