Difference between revisions of "1994 AJHSME Problems/Problem 12"
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<math>\text{(A)}\ 1990 \qquad \text{(B)}\ 1991 \qquad \text{(C)}\ 1992 \qquad \text{(D)}\ 1993 \qquad \text{(E)}\ 1994</math> | <math>\text{(A)}\ 1990 \qquad \text{(B)}\ 1991 \qquad \text{(C)}\ 1992 \qquad \text{(D)}\ 1993 \qquad \text{(E)}\ 1994</math> | ||
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| + | ==Solution== | ||
| + | <math>90=(3)(30)</math> which corresponds to March 30. | ||
| + | |||
| + | <math>91=(7)(13)</math> which corresponds to July 13. | ||
| + | |||
| + | <math>92=(4)(23)</math> which corresponds to April 23. | ||
| + | |||
| + | <math>93=(3)(31)</math> which corresponds to March 31. | ||
| + | |||
| + | <math>94</math> can only be factored into <math>(2)(47)</math>, which does not correspond to any date. The only year that is not lucky is <math>\boxed{\text{(E)}\ 1994}</math>. | ||
| + | ==See Also== | ||
| + | {{AJHSME box|year=1994|num-b=11|num-a=13}} | ||
Revision as of 23:41, 22 December 2012
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
which corresponds to March 30.
which corresponds to July 13.
which corresponds to April 23.
which corresponds to March 31.
can only be factored into 
, which does not correspond to any date. The only year that is not lucky is 
.
See Also
| 1994 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
