1995 AMC 8 Problem 12
Attempt Problem 12 of the 1995 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1995 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
12.
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, is a lucky year because it has the date and Which of the following is NOT a lucky year?
Small hint:
For each year, try to write its last two digits as (month) (day) with a valid month and day
Big hint:
A year fails only when the last two digits cannot be a product of a number at most and a number at most
Solution:
Each of the other years works: and each a valid month/day.
For the last two digits factor only as and is too large for a day (and or is too large for a month). So has no lucky date.
Thus, the correct answer is E .
Problem 12 in other years
- 1985 AMC 8
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