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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

Any idea how can this be solved? I tried repeatedly and failed.

the problem asks you to divide the 1m price of wood in 5 and 3 parts. So think of a baseball bat and you are marking, using a pen, the fifths and thirds. So you would have 1/5, 2/5,3/5, 4/5 marks as well as 1/3 and 2/3 marks.

for comparison reasons you would multiply by fifths by 3 and the thirds by 5. This would give us in order 3/15, 5/15, 6/15, 9/15, 10/15, 12/15.

You can now see that there is 3 3/15 pieces, 2 2/15 pieces and 2 1/15 pieces. In the question, she takes out one piece of each: 1-( 3/15 + 2/15 +1/15 )=1-( 6/15 )= 9/15= 3/5

After the marks on the 1m object. You should have it marked as:3/15, 5/15, 6/15, 9/15, 10/15, 12/15. So the first piece is 3/15-0= 3/15 Second is 5/15- 3/15 = 2/15 Third is 6/15-5/15= 1/15... Last one should be 1-12/15= 3/15

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

Any idea how can this be solved? I tried repeatedly and failed.

This is what you are doing: You are marking off at 1/3, 2/3 and 3/3 and at 1/5, 2/5, 3/5 etc

Or we can say that we are marking at 5/15, 10/15 and 15/15 and at 3/15, 6/15, 9/15 etc so that we can easily compare.

Attachment:

Ques4.jpg [ 3.68 KiB | Viewed 1044 times ]

Now the first piece you get is 3/15 in length, next one is 2/15 and the next one is 1/15. Now think, will you get pieces of length 4/15, 5/15 etc? No because you mark off at every 3/15 (you mark at 3/15, 6/15, 9/15, 12/15 and 15/15). So it is not possible to get any piece which is greater than 3/15.

The length of distinct pieces combined = 1/15 + 2/15 + 3/15 = 6/15 The fraction of original branch that remains = 1 - 6/15 = 9/15 = 3/5 _________________

100 cm long branch will be marked as: 20. 33.33. 40. 60. 66.66. 80 [i. e. you have marking at these points] 1st break: 20 cm, 2nd: 33.33 cm , 3rd: 40 cm and so on

Pieces we will have: 20 cm, 13.33 cm, 6.66 cm, 20 cm, 6.66 cm, 13.33 cm, and 20 cm. Total 100 cm. Length of distinct pieces= 20+13:33+6.66=40 cm Remaining= 100-40= 60. ==>60/100= 3/5

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