1988 AJHSME Problems/Problem 10

Problem

Chris' birthday is on a Thursday this year. What day of the week will it be $60$ days after her birthday?

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

Solutions

Solution 1

7 days after her birthday would be a Thursday, as would 14, 21, 28, 35, 42, 49, and 56. Therefore the 60th would be four days after a Thursday, which is a $\text{Monday} \Rightarrow \mathrm{(A)}$ .

Solution 2

Note that $60\equiv4\pmod7$ . We count 4 days past Thursday, and arrive at Monday. $\mathrm{(A)}$

1988 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
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1988 AJHSME Problems/Problem 10

Contents

Problem

Solutions

Solution 1

Solution 2

See Also