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 "1956 AHSME Problems/Problem 44"

(made question)
 
(Added solution)
 
Line 8: Line 8:
 
\textbf{(D)}\ x^2 > ax\text{ but }ax < 0 \qquad
 
\textbf{(D)}\ x^2 > ax\text{ but }ax < 0 \qquad
 
\textbf{(E)}\ x^2 > a^2\text{ but }a^2 < 0 </math>
 
\textbf{(E)}\ x^2 > a^2\text{ but }a^2 < 0 </math>
 +
 +
== Solution ==
 +
Note that since <math>x</math> and <math>a</math> are negative, <math>x^2, a^2,</math> and <math>ax</math> are all positive. Hence the only correct answer is <math>\fbox{B}</math>.

Latest revision as of 22:17, 7 July 2018

Problem 44

If $x < a < 0$ means that $x$ and $a$ are numbers such that $x$ is less than $a$ and $a$ is less than zero, then:

$\textbf{(A)}\ x^2 < ax < 0 \qquad \textbf{(B)}\ x^2 > ax > a^2 \qquad \textbf{(C)}\ x^2 < a^2 < 0 \\ \textbf{(D)}\ x^2 > ax\text{ but }ax < 0 \qquad \textbf{(E)}\ x^2 > a^2\text{ but }a^2 < 0$

Solution

Note that since $x$ and $a$ are negative, $x^2, a^2,$ and $ax$ are all positive. Hence the only correct answer is $\fbox{B}$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1956_AHSME_Problems/Problem_44&oldid=96012"