2002 AIME I Problems/Problem 3
Problem
Jane is 25 years old. Dick is older than Jane. In years, where is a positive integer, Dick's age and Jane's age will both be two-digit number and will have the property that Jane's age is obtained by interchanging the digits of Dick's age. Let be Dick's present age. How many ordered pairs of positive integers are possible?
Solution
Let Jane's age years from now be , and let Dick's age be . If , then . The possible pairs of are:
That makes 36. But , so we subtract all the extraneous pairs: and .
See also
2002 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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