Question

If today is Saturday then what will be the day on \( 363^{rd} \) day?

• A. \( \text{Sunday} \)
• B. \( \text{Monday} \)
• C. \( \text{Thursday} \)
• D. \( \text{Friday} \)

Hint:

\textbf{Calendar Problems.} In calendar-based reasoning problems, remember that the days of the week repeat every 7 days. To find the day after a certain number of days, divide the number of days by 7 and use the remainder to count forward from the starting day. If the remainder is 0, the day will be the same as the starting day.

Answer 1

The Correct Option is C

The days of the week repeat in a cycle of 7 days. To find the day on the \( 363^{rd} \) day from Saturday, we need to determine how many full cycles of 7 days are there in 363 days and what the remainder is. Divide 363 by 7: $$ 363 \div 7 $$ $$ 363 = 7 \times 51 + 6 $$ This means that there are 51 full weeks and 6 extra days after the \( 363^{rd} \) day. If today is Saturday, then after 7 days it will again be Saturday. After 14 days, it will again be Saturday, and so on. After \( 7 \times 51 = 357 \) days, it will still be Saturday. Now, we need to count forward 6 more days from Saturday: 1st day after Saturday: Sunday 2nd day after Saturday: Monday 3rd day after Saturday: Tuesday 4th day after Saturday: Wednesday 5th day after Saturday: Thursday 6th day after Saturday: Friday Wait, I made a mistake in counting. Let's restart the counting of the 6 extra days from Saturday. If today is Saturday (Day 0), then: Day 1: Sunday Day 2: Monday Day 3: Tuesday Day 4: Wednesday Day 5: Thursday Day 6: Friday So, the day on the \( 363^{rd} \) day will be Friday. Let's re-check the calculation. \( 363 \div 7 \) gives a remainder of 6. If today is Saturday, we need to find the day that is 6 days after Saturday. Saturday + 1 day = Sunday Saturday + 2 days = Monday Saturday + 3 days = Tuesday Saturday + 4 days = Wednesday Saturday + 5 days = Thursday Saturday + 6 days = Friday The day on the \( 363^{rd} \) day will be Friday. There seems to be a discrepancy with the provided correct option. Let me double-check my understanding and calculation. The question asks for the day on the \( 363^{rd} \) day *from today*. If today is considered the 1st day, then the \( 363^{rd} \) day is 362 days *after* today. Let's consider the number of days *after* today: \( 363 - 1 = 362 \) days. Now, find the remainder when 362 is divided by 7: $$ 362 \div 7 $$ $$ 362 = 7 \times 51 + 5 $$ The remainder is 5. So, we need to find the day that is 5 days after Saturday: Saturday + 1 day = Sunday Saturday + 2 days = Monday Saturday + 3 days = Tuesday Saturday + 4 days = Wednesday Saturday + 5 days = Thursday So, if today is Saturday, the day on the \( 363^{rd} \) day will be Thursday. This matches the correct option provided. The key is whether "the day on \( 363^{rd} \) day" means after 363 days from today, or on the day that is numbered 363 if today is day (A) The latter interpretation seems to be the intended one based on the correct answer.