VJesus12 wrote:In a courtyard, one bell rings every 1/4 hour and another bell rings every 1/5 hour. Both bells ring together at exactly the beginning of each hour. Which of the following gives all the intervals that occur between any two rings of the bells in minutes?
A. 6 and 9 only
B. 3, 6 and 9
C. 3, 12 and 15
D. 3, 6, 9 and 12
E. 3, 6, 10 and 12
To make the math easier, let the total timeline = the LCM of the two denominators 4 and 5 = 20 minutes.
Dividing a 20-minute timeline into 5ths and 4ths, we get:
0....4...5...8...10...12...15...16...20.
Each of the values above represents a ring.
The timeline yields the following intervals between successive rings:
4 minutes (from 0 to 4 and from 16 to 20).
1 minute (from 4 to 5 and from 15 to 16).
2 minutes (from 8 to 10 and from 10 to 12).
3 minutes (from 5 to 8 and from 12 to 15).
Since the actual timeline is 60 minutes -- 3 times as long -- the intervals above must all be multiplied by a factor of 3, yielding the following intervals between successive rings:
12 minutes
3 minutes
6 minutes
9 minutes.
The correct answer is
D.
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