1985 AJHSME Problem 20

Problem

In a certain year, January had exactly four Tuesdays and four Saturdays. On what day did January $1$ fall that year?

$\text{(A)}\ \text{Monday} \qquad \text{(B)}\ \text{Tuesday} \qquad \text{(C)}\ \text{Wednesday} \qquad \text{(D)}\ \text{Friday} \qquad \text{(E)}\ \text{Saturday}$

Solution

January has 31 days. If January 1 was on Monday or Tuesday, then there would have been 5 Tuesdays in the month. Similarly, if January 1 was on a Friday or Saturday, then there would have been 5 Saturdays in the month. Therefore, the answer is $\text{(C)}.$

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1985 AJHSME Problem 20

Problem

Solution