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1987 AJHSME Problems/Problem 19

Revision as of 08:12, 14 March 2009 by 5849206328x (talk | contribs) (New page: ==Problem== A calculator has a squaring key <math>\boxed{x^2}</math> which replaces the current number displayed with its square. For example, if the display is <math>\boxed{000003}</mat...)
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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

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