2021 GMC 12B Problems/Problem 1

Problem 1

When $30\%$ of $x$ is a positive perfect square integer, what is $min(x)$ such that $x$ is also an integer?

$\textbf{(A)} ~9 \qquad\textbf{(B)} ~12 \qquad\textbf{(C)} ~30 \qquad\textbf{(D)} ~36 \qquad\textbf{(E)} ~120$

Solution

Let $s$ be the perfect square. For $30\%$ of $x$ to be $s$ , $x = \dfrac{10}3 s$ . Thus, $s$ is the first perfect square that is divisble by $3$ , or in other words, $s = 9$ . Since $x = \dfrac{10}3s$ , $x = \boxed{\textbf{(C)}~30}$ .

~pineconee

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2021 GMC 12B Problems/Problem 1

Problem 1

Solution