Difference between revisions of "1997 AIME Problems"
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== Problem 4 == | == Problem 4 == | ||
| + | Circles of radii 5, 5, 8, and <math>m/n</math> are mutually externally tangent, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m + n.</math> | ||
[[1997 AIME Problems/Problem 4|Solution]] | [[1997 AIME Problems/Problem 4|Solution]] | ||
Revision as of 12:33, 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?
Problem 4
Circles of radii 5, 5, 8, and 
are mutually externally tangent, where and are relatively prime positive integers. Find
