Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

(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...)
 
m
Line 1: Line 1:
 
==Problem==
 
==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}</math> and the <math>\boxed{x^2}</math> key is depressed, then the display becomes <math>\boxed{000009}</math>.  If the display reads <math>\boxed{000002}</math>, how many times must you depress the <math>\boxed{x^2}</math> key to produce a displayed number greater than <math>500</math>?
+
A calculator has a squaring key <math>\boxed{x^2}</math> which replaces the current number displayed with its [[Perfect square|square]].  For example, if the display is <math>\boxed{000003}</math> and the <math>\boxed{x^2}</math> key is depressed, then the display becomes <math>\boxed{000009}</math>.  If the display reads <math>\boxed{000002}</math>, how many times must you depress the <math>\boxed{x^2}</math> key to produce a displayed number greater than <math>500</math>?
  
 
<math>\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 250</math>
 
<math>\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 250</math>
Line 19: Line 19:
 
==See Also==
 
==See Also==
  
−
[[1987 AJHSME Problems]]
+
{{AJHSME box|year=1987|num-b=18|num-a=20}}
 +
[[Category:Introductory Algebra Problems]]

Revision as of 18:38, 30 May 2009

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 • 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
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1987_AJHSME_Problems/Problem_19&oldid=31943"