A 1 meter tree limb was divided and labeled by fifths and sixths. The

Hi,

I fail to understand the last part :
Lengths of pieces will be difference of immediate terms..
So 30, 6, 24, 12, 18, 12, 24, 6, 30
Lengths between 9 and 20
12, 18, 18, 12 -- so 4 pieces.


Please can you elaborate?

Solution:

The markings on the tree limb, by fifths, are 1/5, 2/5, 3/5, and 4/5. Similarly, the markings by sixths are 1/6, 2/6 = 1/3, 3/6 = 1/2, 4/6 = 2/3, and 5/6. Including 0 and 1 (the two ends of the limb) and arranging these numbers in ascending order, we have:

0, 1/6, 1/5, 1/3, 2/5, 1/2, 3/5, 2/3, 4/5, 5/6, 1

Now, let’s find the difference of every pair of consecutive numbers (i.e., 1/6 - 0, 1/5 - 1/6, 1/3 - 1/5, etc.):

1/6, 1/30, 2/15, 1/15, 1/10, 1/10, 1/15, 2/15, 1/30, 1/6

The numbers in the above list are the lengths of the 10 pieces that the limb wascut into. Of these numbers, 1/6 and 2/15 are greater than 1/9, and 1/30 is less than 1/20. Thus, they are not between 1/9 and 1/20. The remaining 4 numbers (two 1/15’s and two 1/10’s) are in that interval. So 4 pieces are kept.

Answer: C

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