Difficulty: Easy
Correct Answer: Saturday
Explanation:
Introduction:
This is a straightforward modular arithmetic calendar question. When asked what day it will be a certain number of days from now, we use the fact that days of the week repeat every 7 days. The key is to reduce the given number of days modulo 7 and then shift the weekday accordingly.
Given Data / Assumptions:
Today's day: Saturday. Number of days ahead: 350 days. Week has 7 days and repeats cyclically.
Concept / Approach:
The day of the week after N days is determined by N modulo 7, because every block of 7 days brings you back to the same weekday. If N is exactly divisible by 7, then the weekday after N days will be the same as today. If there is a remainder r, then we move r days forward in the weekly cycle.
Step-by-Step Solution:
Step 1: Compute N modulo 7. N = 350 days. 350 ÷ 7 = 50 with remainder 0. So 350 ≡ 0 (mod 7). Step 2: Interpret the remainder. A remainder of 0 means that 350 days equals exactly 50 full weeks. After any whole number of weeks, the day of the week is unchanged. Step 3: Apply to the starting day. Starting on Saturday and moving ahead exactly 50 weeks, we return to Saturday.
Verification / Alternative check:
You can check with a smaller example: after 7 days from a Saturday, it is again Saturday; after 14 days, also Saturday, and so on. 350 is simply a larger multiple of 7 (7 * 50), so the same logic applies. This confirms that the weekday does not change.
Why Other Options Are Wrong:
Friday, Sunday, Monday, Thursday: These would all be correct only if the total days ahead left a remainder of 1, 2, 3, or 4 when divided by 7. Since 350 leaves no remainder, there is no shift from Saturday.
Common Pitfalls:
Sometimes students try to move forward week by week manually or miscalculate 350 ÷ 7, leading to an incorrect remainder. Always reduce the number of days modulo 7 to avoid errors and save time.
Final Answer:
350 days from a Saturday will again be a Saturday.
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