2023 AMC 8 Problems/Problem 6

Problem

The digits 2, 0, 2, and 3 are placed in the expression below, one digit per box. What is the maximum possible value of the expression?

$\textbf{(A) }0 \qquad \textbf{(B) }8 \qquad \textbf{(C) }9 \qquad \textbf{(D) }16 \qquad \textbf{(E) }18$

Solution 1

First, let us consider the cases where $0$ is a base. This would result in the entire expression being $0$ . However, if $0$ is an exponent, we will get a value greater than $0$ . As $3^2\cdot2^0=9$ is greater than $2^3\cdot2^0=8$ and $2^2\cdot3^0=4$ , the answer is $\boxed{\textbf{(C) }9}$ .

~MathFun1000

Solution 2

The maximum possible value of using the digit $2,0,2,3$ . We can maximize our value by keeping the $3$ and $2$ together in one power. (Biggest with biggest and smallest with smallest) This shows $3^{2}*2^{0}$ = $9*1$ = $9$ . (Don't want $0^{2}$ because that is $0$ ) It is going to be $\boxed{\text{(C)}9}$

~apex304 (SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, stevens0209, ILoveMath31415926535 (editing))

Video Solution by Magic Square

https://youtu.be/-N46BeEKaCQ?t=5247

2023 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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All AJHSME/AMC 8 Problems and Solutions

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2023 AMC 8 Problems/Problem 6

Contents

Problem

Solution 1

Solution 2

Video Solution by Magic Square

See Also