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 "1979 AHSME Problems/Problem 13"

(Created page with "== Problem 13 == The inequality <math>y-x<\sqrt{x^2}</math> is satisfied if and only if <math>\textbf{(A) }y<0\text{ or }y<2x\text{ (or both inequalities hold)}\qquad \tex...")
 
m (→‎Solution)
 
(One intermediate revision by the same user not shown)
Line 12: Line 12:
 
Solution by e_power_pi_times_i
 
Solution by e_power_pi_times_i
  
−
<math>\sqrt{x^2} = \pmx</math>, so the inequality is just <math>y-x<\pmx</math>. Therefore we get the two inequalities <math>y<0</math> and <math>y<2x</math>. Checking the answer choices, we find that <math>\boxed{\textbf{(A) } y<0\text{ or }y<2x\text{ (or both inequalities hold)}}</math>.
+
<math>\sqrt{x^2} = \pm x</math>, so the inequality is just <math>y-x<\pm x</math>. Therefore we get the two inequalities <math>y<0</math> and <math>y<2x</math>. Checking the answer choices, we find that <math>\boxed{\textbf{(A) } y<0\text{ or }y<2x\text{ (or both inequalities hold)}}</math> is the answer.
  
 
== See also ==
 
== See also ==

Latest revision as of 12:05, 6 January 2017

Problem 13

The inequality $y-x<\sqrt{x^2}$ is satisfied if and only if

$\textbf{(A) }y<0\text{ or }y<2x\text{ (or both inequalities hold)}\qquad \textbf{(B) }y>0\text{ or }y<2x\text{ (or both inequalities hold)}\qquad \textbf{(C) }y^2<2xy\qquad \textbf{(D) }y<0\qquad \textbf{(E) }x>0\text{ and }y<2x$

Solution

Solution by e_power_pi_times_i

$\sqrt{x^2} = \pm x$, so the inequality is just $y-x<\pm x$. Therefore we get the two inequalities $y<0$ and $y<2x$. Checking the answer choices, we find that $\boxed{\textbf{(A) } y<0\text{ or }y<2x\text{ (or both inequalities hold)}}$ is the answer.

See also

1979 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 12 		Followed by
Problem 14
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 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1979_AHSME_Problems/Problem_13&oldid=82210"