Difference between revisions of "1987 AJHSME Problems/Problem 19"

Revision as of 19:42, 30 October 2016

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: $\begin{align*} 2 &\rightarrow 4 \\ &\rightarrow 16 \\ &\rightarrow 256 \\ &\rightarrow 512>500 \end{align*}$

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
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
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

Difference between revisions of "1987 AJHSME Problems/Problem 19"

Revision as of 19:42, 30 October 2016

Problem

Solution

See Also

@@ Line 12: / Line 12: @@
 &\rightarrow 16 \\
 &\rightarrow 256 \\
-&\rightarrow 65536>500
+&\rightarrow 512>500
 \end{align*}</cmath>