1995 AJHSME Problems/Problem 12
Problem
A lucky year is one in which at least one date, when written in the form month/day/year, has the following property: The product of the month times the day equals the last two digits of the year. For example, 1956 is a lucky year because it has the date 7/8/56 and . Which of the following is NOT a lucky year?
Solution
We examine only the factors of and that are less than , because for a year to be lucky, it must have at least one factor between and to represent the month.
has factors of and . Dividing by the last number , gives . Thus, is a valid date, and is a lucky year.
has factors of and . Dividing by gives , and is a valid date. Thus, is a lucky year.
has factors of and . Dividing by gives , and is a valid date. Thus, is a lucky year.
has factors of and . Dividing by gives , and is a valid date. Thus, is a lucky year.
has factors of and . Dividing by gives , and no month has days. Thus, is not a lucky year, and the answer is .
See Also
1995 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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