AoPSWiki

Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.

Personal tools

Search

Toolbox

University of South Carolina High School Math Contest/1993 Exam/Problem 9

From AoPSWiki

Problem

Suppose that $x$ and $y$ are integers such that $y > x > 1$ and $y^2 - x^2 = 187$ . Then one possible value of $xy$ is

$\mathrm{(A) \ }30 \qquad \mathrm{(B) \ }36 \qquad \mathrm{(C) \ }40 \qquad \mathrm{(D) \ }42 \qquad \mathrm{(E) \ }54$

Solution

We have $(y+x)(y-x)=187$ . Now, $187=11 \cdot 17$ , so we have as one possibility $y+x=17$ and $y-x=11$ . Thus, $x=3, y=14$ is a possible solution and the answer is $42$ .

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/University_of_South_Carolina_High_School_Math_Contest/1993_Exam/Problem_9"

Category: Introductory Algebra Problems

Try our innovative online adaptive learning system, Alcumus.
Over 1100 problems and 60+ video lessons. FREE!

© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us