2023 AMC 12A Problems/Problem 3

Problem

How many positive perfect squares less than $2023$ are divisible by $5$ ?

$\textbf{(A) } 8 \qquad\textbf{(B) }9 \qquad\textbf{(C) }10 \qquad\textbf{(D) }11 \qquad\textbf{(E) } 12$

Solution 1

Note that $40^2=1600$ but $45^{2}=2025$ (which is over our limit of $2023$ ) so the list is $5^2,10^2,15^2,20^2,25^2,30^2,35^2,40^2$ . There are $8$ elements, so the answer is $\boxed{\textbf{(A) 8}}$ .

~zhenghua

(Minor edits for clarity by Technodoggo)

Solution 2 (slightly refined)

Since $\left \lfloor{\sqrt{2023}}\right \rfloor = 44$ , there are $\left \lfloor{\frac{44}{5}}\right \rfloor = \boxed{\textbf{(A) 8}}$ perfect squares less than 2023.

~not_slay

2023 AMC 10A (Problems • Answer Key • Resources)
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2023 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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All AMC 12 Problems and Solutions

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2023 AMC 12A Problems/Problem 3

Contents

Problem

Solution 1

Solution 2 (slightly refined)

See Also