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

Question

A 1 meter tree limb was divided and labeled by fifths and sixths. The limb was then cut at each label. If pieces between  \frac{1}{9}  and  \frac{1}{20}  of a meter are kept, how many pieces are kept?

a. 0

b. 2

c. 4

d. 6

e. 30

chetan2u · Accepted Answer

Let us make it easy by taking smart number and that will be the LCM of 9 and 20 here..
So the entire length will be 180..
It is cut at fifths so 180/5=36, so cuts at 36, 72, 108, 144 and 180
and sixths so 180/6=30, so cuts at 30, 60, 90, 120, 150 and 180...

When combined ... 30, 36, 60, 72, 90, 108, 120, 144, 150 and 180..
We are looking for pieces between lengths of 180/9=20 and 180/20=9,so 9 and 20

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.

C

Archit3110 · Answer

chetan2u really an amazing solution to the problem you have given... i honestly struggled for 2 mins trying to find way to solve , ended up in fractions..

.. thanks

pg03 · Answer

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?

ScottTargetTestPrep · Answer

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

RahulVohra · Answer

chetan2u  please let me know whether my way of solving this question is correct or not:

Since the label were cut between 1/9 and 1/20.

we know that 1/9 = 0.1111.... and 1/20 = 0.05
 
we need to find approx between 0.05 and 0.1.

so 0.06,0.07,0.08,0.09 are between 0.05 and 0.1

Hence 4 pieces

Kinshook · Answer

AkshdeepS

A 1 meter tree limb was divided and labeled by fifths and sixths. The limb was then cut at each label. If pieces between  \frac{1}{9}  and  \frac{1}{20}  of a meter are kept, how many pieces are kept?

1/9 = 20/180; 1/20 = 9/180

Labels of fifths = {0,1/5,2/5,3/5,4/5,5/5=1}
Labels of sixths = {0,1/6,2/6=1/3,3/6=1/2,4/6=2/3,5/6,6/6=1}

Arranging labels in increasing order = {0,1/6,1/5,1/3,2/5,1/2,3/5,2/3,4/5,5/6,1}

Lengths of pieces: - 
1/6 - 0 = 1/6 = 30/180; Big; Not kept
1/5- 1/6 = 1/30 = 6/180; Small; Not kept
1/3 - 1/5 = 2/15 = 24/180; Big; Not kept
 2/5 - 1/3 = 1/15 = 12/180; Kept 
 1/2 - 2/5 = 1/10 = 18/180; Kept 
 3/5 - 1/2 = 1/10 = 18/180; Kept 
 2/3 - 3/5 = 1/15 = 12/180 ; Kept 
4/5 - 2/3 = 2/15 = 24/180; Big; Not Kept
5/6 - 4/5 = 1/30 = 6/180; Small; Not Kept
1-5/6 = 1/6 = 30/180; Big; Not Kept

4 pieces are kept

IMO C

chetan2u · Answer

May not be the correct way. The piece could be 0.066 or 0.061 too

SkyBulb · Answer

5th cuts for 100cm rod - 20 / 40 / 60 / 80
6th cuts for 100cm rod (rough estimate) - 16.6 / 33.2 / 49.8 / 66.4 / 84

1/9 - 11.11 cm
1/20 - 5cm

so we pick 4 rods (there is possibility of error if answer were close though)

PineToad · Answer

I find converting the fractions to percentages here to be most intuitive for me. 
We want pieces that are between  5 % of a meter and  11 % of a meter in length.

If we convert every fifth to percents, we get 20, 40, 60, 80, 100
Likewise every sixth is 17, 33, 50, 67, 83, 100 (roughly).

Now pair them in order.
The first piece will be between points 0 and 17. We won't keep this because the length is 17 and we only want lengths between 5 and 11.
The second piece between 17 and 20. We won't keep this because the length is 3, which is less than 5.

And so on:
20 and 33 (discard)
33 and 40 (keep)
40 and 50 (keep)
50 and 60 (keep)
60 and 67 (keep)
67 and 80 (discard)
80 and 83 (discard)
83 and 100 (discard)

4 keeps.

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

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

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