Question

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 $7 \times 8 = 56.$ Which of the following is NOT a lucky year?

$1990$

$1991$

$1992$

$1993$

$1994$

Solution:

Each of the other years works: $90 = 9 \times 10,$ $91 = 7 \times 13,$ $92 = 4 \times 23,$ and $93 = 3 \times 31,$ each a valid month/day.

For $1994,$ the last two digits factor only as $94 = 2 \times 47,$ and $47$ is too large for a day (and $94$ or $47$ is too large for a month). So $1994$ has no lucky date.

Thus, the correct answer is E .

1995 AMC 8 Problem 12

Solution:

Problem 12 in Other Years