2017 AMC 10B Problems/Problem 6

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Problem

What is the largest number of solid $2\text{ in}$ by $2\text{ in}$ by $1\text{ in}$ blocks that can fit in a $3\text{ in}$ by $2\text{ in}$ by $3\text{ in}$ box?

$\textbf{(A)}\ 3\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7$

Solution

We find that the volume of the larger block is $18$, and the volume of the smaller block is $4$. Dividing the two, we see that only a maximum of $4$ $2$x$2$x$1$ blocks can fit inside the $3$x$3$x$2$ block. $\boxed{\textbf{(B) }4}$


2017 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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