1994 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 $7\times 8 = 56$ . Which of the following is NOT a lucky year?

$\text{(A)}\ 1990 \qquad \text{(B)}\ 1991 \qquad \text{(C)}\ 1992 \qquad \text{(D)}\ 1993 \qquad \text{(E)}\ 1994$

Solution

$90=(3)(30)$ which corresponds to March 30.

$91=(7)(13)$ which corresponds to July 13.

$92=(4)(23)$ which corresponds to April 23.

$93=(3)(31)$ which corresponds to March 31.

$94$ can only be factored into $(2)(47)$ , which does not correspond to any date. The only year that is not lucky is $\boxed{\text{(E)}\ 1994}$ .

1994 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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1994 AJHSME Problems/Problem 12

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