2020 AMC 10B Problems/Problem 24

Problem

How many positive integers $n$ satisfy $\dfrac{n+1000}{70} = \lfloor \sqrt{n} \rfloor?$ (Recall that $\lfloor x\rfloor$ is the greatest integer not exceeding $x$ .)

$\textbf{(A) } 2 \qquad\textbf{(B) } 4 \qquad\textbf{(C) } 6 \qquad\textbf{(D) } 30 \qquad\textbf{(E) } 32$

Solution

Wolfram Alpha shows that there must be $6$ solutions: $n=400, 470, 2290, 2360, 2430, 2500$

That doesn't count. -QuadraticFunctions

2020 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 23	Followed by Problem 25
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2020 AMC 10B Problems/Problem 24

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