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1987 AJHSME Problems/Problem 19

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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}}

See Also

1987 AJHSME (Problems • Resources)
Preceded by
Problem 18 		Followed by
Problem 20
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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