1991 AIME Problems/Problem 5
Problem
Given a rational number, write it as a fraction in lowest terms and calculate the product of the resulting numerator and denominator. For how many rational numbers between and will be the resulting product?
Solution
If the fraction is in the form , then and . There are 8 prime numbers less than 20 (), and each can only be a factor of one of or . There are ways of selecting some combination of numbers for ; however, since , only half of them will be between . Therefore, the solution is .
See also
1991 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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