Problem 16 · 2012 Math Kangaroo
Hard
Logic & Word Problems
caseworkwork-backward
On each of the four walls in Billy's room hangs a correctly working clock, but each one runs either behind or ahead of the correct time. The first clock is incorrect by 2 minutes, the second by 3 minutes, the third by 4 minutes and the fourth by 5 minutes. Billy wants to know what time it is and sees the following times: 6 minutes to 3, 3 minutes to three, 2 minutes past three and 3 minutes past 3. What is the actual time?
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Answer: D — 2:59
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Hint 1 of 2
Write each shown time as minutes before/after 3:00, and the errors are 2, 3, 4, 5.
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Hint 2 of 2
Find one true time so the four gaps to the shown times are exactly 2, 3, 4, 5.
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Approach: match the shown times to the four error sizes
- The shown times are 6 to 3, 3 to 3, 2 past 3, 3 past 3, i.e. −6, −3, +2, +3 minutes from 3:00.
- Try the true time 2:59 (one minute before 3:00): the gaps become 5, 2, 3, 4 minutes.
- Those are exactly the four errors 2, 3, 4 and 5, each used once, so the true time is 2:59 (D).
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