1999 CEMC Pascal Problems/Problem 11

Problem

Today is Wednesday. What day of the week will it be $100$ days from now?

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

Solution

The days of the week repeat every $7$ days. Thus, we can see what the remainder is when dividing $100$ by $7$ is, and add however many days we need to Wednesday.

$7 \times 14 = 98$ , but $7 \times 15 = 105$ . This means that the quotient must be $14$ .

$100$ is $2$ more than $98$ , so we need to see what day of the week is $2$ days after Wednesday.

$2$ days after Wednesday is $\boxed {\textbf {(D) } \text{Friday}}$ .

~anabel.disher

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1999 CEMC Pascal Problems/Problem 11

Problem

Solution