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2018 AMC 10B Problem 1

2018 AMC 10B Problem 1AMC 10 Step by Step

Name: Date: September 13, 2026

Basic Counting · difficulty 1 of 5 · about 1 min · position P1-10

Kate bakes a $20$ -inch by $18$ -inch pan of cornbread. The cornbread is cut into pieces that measure $2$ inches by $2$ inches. How many pieces of cornbread does the pan contain?

A)
$90$
B)
$100$
C)
$180$
D)
$200$
E)
$360$

Answer

Key insight

Each side of the pan holds a whole number of 2-inch pieces: 20/2 = 10 across and 18/2 = 9 down, so 10 times 9 pieces.

Solution

Along the $20$ -inch side the pan is cut into $20/2 = 10$ pieces; along the $18$ -inch side into $18/2 = 9$ pieces. Since both dimensions divide evenly, the pieces form a $10 \times 9$ grid with nothing left over:
$10 \cdot 9 = 90.$

The answer is $\boxed{\textbf{(A)}\ 90}$ .

Why this works

Counting a grid is the multiplication principle: (pieces per row) times (number of rows). Always check that the piece size divides each dimension; when it does, dividing areas ( $360/4 = 90$ ) gives the same count, but when it does not, only the row-by-column count is trustworthy.

Alternative approach

Divide areas: the pan has $20 \cdot 18 = 360$ square inches and each piece has $4$ , so $360/4 = 90$ .

The trap

Dividing the total area 360 by 2 (the side of a piece) instead of by the piece area 4, giving 180.

Common mistakes

Dividing the total area 360 by 2 (the side of a piece) instead of by the piece area 4, giving 180.
Adding $10 + 9$ or computing $20 \cdot 18 / 2 / 2$ with an arithmetic slip; the choices $180$ and $360$ are there to catch exactly that.

Techniques

Set up the equation/formula and compute; no special trick needed