2012 AMC 10B Problems/Problem 10
Contents
[hide]Problem
How many ordered pairs of positive integers satisfy the equation
Solution 1
Cross-multiplying gives We write as a product of two positive integers: The products and each produce ordered pairs as we can switch the order of the factors. The product produces ordered pair Together, we have ordered pairs
~Rguan (Solution)
~MRENTHUSIASM (Reformatting)
Solution 2
Cross-multiplying gives From the prime factorization we conclude that has positive divisors. There are values of and each value generates ordered pair So, there are ordered pairs in total.
~MRENTHUSIASM
See Also
2012 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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All AMC 10 Problems and Solutions |
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