# Difference between revisions of "1997 AIME Problems"

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== Problem 3 == | == Problem 3 == | ||

+ | Sarah intended to multiply a two-digit number and a three-digit number, but she left out the multiplication sign and simply placed the two-digit number to the left of the three-digit number, thereby forming a five-digit nmber. This number is exactly nine times the product Sarah should have obtained. What is the sum of the two-digit number and the three-digit number? | ||

[[1997 AIME Problems/Problem 3|Solution]] | [[1997 AIME Problems/Problem 3|Solution]] |

## Revision as of 10:21, 11 October 2007

## Contents

## Problem 1

How many of the integers between 1 and 1000, inclusive, can be expressed as the difference of the squares of two nonnegative integers?

## Problem 2

The nine horizontal and nine vertical lines on an checkeboard form rectangles, of which are squares. The number can be written in the form where and are relatively prime positive integers. Find

## Problem 3

Sarah intended to multiply a two-digit number and a three-digit number, but she left out the multiplication sign and simply placed the two-digit number to the left of the three-digit number, thereby forming a five-digit nmber. This number is exactly nine times the product Sarah should have obtained. What is the sum of the two-digit number and the three-digit number?