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 11:21, 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?