1970 AMC 12 Problem 29
Attempt Problem 29 of the 1970 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1970 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
29.
It is now between and o’clock, and six minutes from now, the minute hand of a watch will be exactly opposite the place where the hour hand was three minutes ago. What is the exact time now?
Answer: D
Small hint:
Let be the number of minutes after now
Big hint:
In minute-space units, the future minute hand is at , while the point opposite the past hour hand is at
Solution:
Let be the number of minutes after now. Six minutes from now, the minute hand is minute spaces clockwise from Three minutes ago, the hour hand was minute spaces past the so the point opposite it was minute spaces past Hence Solving gives so the time is
Therefore, the correct answer is D.
Problem 29 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
- 1960 AMC 12
- 1961 AMC 12
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- 1963 AMC 12
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- 1967 AMC 12
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- 1969 AMC 12
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- 1976 AMC 12
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