KA-0021Remainders and modular cycles
3 points, difficulty 1 of 3Level 5–6about 45sToday is Tuesday. What day of the week will it be in 100 days?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Days repeat every seven.
2The strategy
Only the remainder when you divide by 7 matters, because 7 days always brings you back to the same weekday. Work out that remainder and count that many days forward.
3The full solution
100 divided by 7 is 14 remainder 2. Fourteen whole weeks land back on Tuesday, and 2 more days is Thursday.
Solution— no shortcut on this one
Weekdays repeat every 7 days, so divide 100 by 7: that is 14 remainder 2. The 14 whole weeks bring you back to Tuesday, and then 2 more days gives Wednesday, Thursday. The answer is Thursday. The transferable idea: with anything cyclic, throw away the whole cycles and keep only the remainder.
Why this is on the test: Calendar questions are remainder questions in disguise, and using the quotient instead of the remainder is the standard slip.