Difficulty: Easy
Correct Answer: Sunday
Explanation:
Introduction:
This problem asks for the weekday 65 days from a known weekday, Friday. It is a typical example of using the modulo 7 concept for calendar calculations, because the days of the week repeat every 7 days.
Given Data / Assumptions:
Today: Friday. Days ahead: 65 days. We use a 7-day repeating weekly cycle.
Concept / Approach:
The weekday after N days is obtained by moving forward N modulo 7 positions in the weekday cycle. That is, we compute the remainder when N is divided by 7. If the remainder is r, then we move r days forward from the starting day to find the target day of the week.
Step-by-Step Solution:
Step 1: Compute 65 modulo 7. 65 ÷ 7 = 9 with remainder 2 (since 7 * 9 = 63). So 65 ≡ 2 (mod 7). Step 2: Interpret the remainder. A remainder of 2 means that 65 days correspond to 9 full weeks plus 2 extra days. Full weeks do not change the weekday; only the extra 2 days matter. Step 3: Move 2 days forward from Friday. Friday + 1 day = Saturday. Saturday + 1 day = Sunday. Thus, 65 days from Friday is Sunday.
Verification / Alternative check:
We can cross-check with a smaller equivalent number of days. Since 65 ≡ 2 (mod 7), the weekday 65 days from Friday is the same as the weekday 2 days from Friday. Counting 2 days ahead gives Sunday, confirming our result without enumerating all 65 days.
Why Other Options Are Wrong:
Saturday: This would be correct for a remainder of 1, not 2. Friday: This would require a remainder of 0 (a full number of weeks). Thursday: This corresponds to moving back by 1 day from Friday, not forward by 2. Monday: This would require a remainder of 3, not 2.
Common Pitfalls:
Students sometimes miscalculate 65 ÷ 7 or mistakenly move backward instead of forward in the weekday cycle. Others forget that any multiple of 7 days does not change the weekday, so they overcomplicate the problem instead of focusing on the remainder.
Final Answer:
65 days from Friday, it will be Sunday.
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