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09 Jun 2021, 06:45
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
48% (02:02) correct
52%
(02:36)
wrong
based on 27
sessions
History
Date
Time
Result
Not Attempted Yet
At what time between 3 pm and 4 pm will the angle between the two hands of a clock be equal to 50°?
(A) 7 and 3/11 min past 3 pm
(B) 25 and 5/11 min past 3 pm
(C) 27 and 2/11 min past 3 pm
(D) Both A and B
(E) None of the above
(A) 7 and 3/11 min past 3 pm
(B) 25 and 5/11 min past 3 pm
(C) 27 and 2/11 min past 3 pm
(D) Both A and B
(E) None of the above
09 Jun 2021, 10:09
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Bunuel
One rotation is 360 degrees, so between each hour we have 30 degrees each. At 3 pm the hour hand would be at 90 degrees away from the top.
The hour hand travels at \(360*\frac{1}{60}*\frac{1}{12} = 0.5\) degrees per minute, while the minute angle travels \(360*\frac{1}{60} = 6\) degrees per minute. Set x as the number of minutes needed to create the 50-degree angle. Treat the "degrees" as distance, and we would have a normal distance/speed problem, where the minute hand has a speed of 6x, and the hour angle has a speed of 0.5x but starts at 90.
There are two scenarios where the hands make an angle of 50 degrees (if you want to go for a wild guess we can choose D already since we're supposed to get two values):
(1) When the minute hand catches up and closes the 90-degree angle until it reaches 50 degrees.
\(6*x + 50 = 90 + 0.5x\) and \(x = \frac{40}{5.5} = \frac{80}{11} = 7\frac{3}{11}\)
(2) When the minute hand surpasses the hour hand and then creates a 50-degree angle.
\(6x = 90 + 0.5x + 50 = 140 + 0.5x\) and \(5.5x = 140\). Then \(x = \frac{140}{5.5} = \frac{280}{11} = 25\frac{5}{11}\)
Thus the values in A and B are both correct, we choose D.
Ans: D
