1987 AJHSME Problems/Problem 19

Problem

A calculator has a squaring key $\boxed{x^2}$ which replaces the current number displayed with its square. For example, if the display is $\boxed{000003}$ and the $\boxed{x^2}$ key is depressed, then the display becomes $\boxed{000009}$ . If the display reads $\boxed{000002}$ , how many times must you depress the $\boxed{x^2}$ key to produce a displayed number greater than $500$ ?

$\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 250$

Solution

We just brute force this: $\begin{align*} 2 &\rightarrow 4 \\ &\rightarrow 16 \\ &\rightarrow 256 \\ &\rightarrow 65536>500 \end{align*}$

Clearly we need to press the button $4$ times, so $\boxed{\text{A}}$

1987 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 18	Followed by Problem 20
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1987 AJHSME Problems/Problem 19

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