Problem 5 · 2002 AMC 8
Easy
Number Theory
divisibility
Carlos Montado was born on Saturday, November 9, 2002. On what day of the week will Carlos be 706 days old?
Show answer
Answer: C — Friday.
Show hints
Hint 1 of 2
Whole weeks change nothing — 7 days later is the same weekday. So toss out the full weeks and only the *leftover* days matter.
Still stuck? Show hint 2 →
Hint 2 of 2
Split 706 cleverly: 706 = 700 + 6, and 700 is a clean stack of weeks (7 × 100). That leaves just 6 days to walk forward.
Show solution
Approach: strip off the whole weeks (multiples of 7)
- The weekday repeats every 7 days, so anything that's a multiple of 7 is invisible. Peel 706 into 700 + 6: those 700 days are exactly 100 weeks and land you right back on Saturday.
- Now just step 6 days past Saturday: Sun, Mon, Tue, Wed, Thu, Friday.
- *The reusable trick:* for any "what day/position after N steps" question with a cycle of length 7, only the *leftover* of N after pulling out whole cycles matters — break N into (multiple of 7) + (small remainder).
Mark:
· log in to save