Discussion

If the third day of a month is Tuesday, which of the following would be the 25th day of that month?

Answer: C

Count forward from the given day and reduce modulo 7:

\[ 25 - 3 = 22 \text{ days} \]

\[ 22 = 3 \times 7 + 1 \quad\Longrightarrow\quad 22 \equiv 1 \pmod 7 \]

So the 25th is one day past the day of the 3rd:

\[ \text{Tuesday} + 1 = \textbf{Wednesday} \]

Listing them confirms it: the Tuesdays are the 3rd, 10th, 17th and 24th, so the 25th is the Wednesday that follows.

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