Problem 11 · 2011 Math Kangaroo
Stretch
Logic & Word Problems
divisibilitycasework
In a certain month there were 5 Mondays, 5 Tuesdays and 5 Wednesdays. In the month before there were only 4 Sundays. What will be true in the next month?
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Answer: B — exactly 4 Saturdays
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Hint 1 of 2
Five Mondays, Tuesdays and Wednesdays force a 31-day month starting on a Monday.
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Hint 2 of 2
Use 'the previous month had only 4 Sundays' to identify the month, then look at the one after.
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Approach: pin down the month, then read off the next one
- Five each of Mon/Tue/Wed means a 31-day month beginning on Monday (so it ends on a Wednesday).
- The previous month ended on a Sunday with only 4 Sundays, which only fits a 28-day February — so this month is March.
- Next is April (30 days) starting on Thursday: its Saturdays fall on the 3rd, 10th, 17th and 24th.
- That is exactly 4 Saturdays, choice (B).
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