1992 AIME Problems/Problem 1

Problem

Find the sum of all positive rational numbers that are less than 10 and that have denominator 30 when written in lowest terms.

Solution

There are 8 fractions which fit the conditions between 0 and 1:

Their sum is 4. Note that there are also 8 terms between 1 and 2 which we can obtain them by adding 1 to each of our first 8 terms. For example, Following this pattern, our answer is

[[{{{year}}} AIME ]] ([[{{{year}}} AIME Problems|Problems]] • [[{{{year}}} AIME Answer Key|Answer Key]] • Resources)
Preceded by First question	Followed by [[{{{year}}} AIME Problems/Problem 2|Problem 2]]
[[{{{year}}} AIME Problems/Problem 1|1]] • [[{{{year}}} AIME Problems/Problem 2|2]] • [[{{{year}}} AIME Problems/Problem 3|3]] • [[{{{year}}} AIME Problems/Problem 4|4]] • [[{{{year}}} AIME Problems/Problem 5|5]] • [[{{{year}}} AIME Problems/Problem 6|6]] • [[{{{year}}} AIME Problems/Problem 7|7]] • [[{{{year}}} AIME Problems/Problem 8|8]] • [[{{{year}}} AIME Problems/Problem 9|9]] • [[{{{year}}} AIME Problems/Problem 10|10]] • [[{{{year}}} AIME Problems/Problem 11|11]] • [[{{{year}}} AIME Problems/Problem 12|12]] • [[{{{year}}} AIME Problems/Problem 13|13]] • [[{{{year}}} AIME Problems/Problem 14|14]] • [[{{{year}}} AIME Problems/Problem 15|15]]
All AIME Problems and Solutions