swerve wrote:Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?
A. 2/5
B. 7/15
C. 1/2
D. 8/15
E. 3/5
Ignore the given length of 1-meter. The problem can be solved using any length.
Let length = 15 meters.
Dividing 15 into 3rds will yield markings at 5 and 10.
Dividing 15 into 5ths will yield markings at 3, 6, 9, and 12.
Listing the markings in order:
0......3....5..6......9..10....12......15
There are only 3 distinct lengths: 1 meter, 2 meters, and 3 meters.
Subtracting these 3 distinct lengths from 15, we get:
Length remaining = 15-1-2-3 = 9.
Remaining length/Total length = 9/15 = 3/5.
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