fractions 700 level question

[mukund_nair]

Hi All,
I've trying to review a cat exam and here is a problem that I got incorrect.
I don't really understand the explanation the way it is worded. Can someone break it down ?
I have attached my explanation at how I arrived at the answer while reviewing. Does it match the official explanation ? I cannot reproduce the image-figure in the explanation.
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Question
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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?
Answer choices are
2/5
7/15
1/2
8/15
3/5

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Solution (minus the diagram)
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In this Fractions problem, a 1-meter branch is marked in thirds and fifths. Because it’s difficult to compare, add, and subtract intervals with thirds and fifths, we can write the fractions in terms of the common denominator, 15. We can draw the following diagram to help us visualize each segment of the branch and quickly calculate the lengths of each interval.



We see from the figure that the unique lengths of the segments are . The total length of the pieces taken away is when simplified. The fraction of the original branch that remains is therefore .

Note that if we removed the three segments of unique lengths from the right end of the branch, we can quickly see that the length of the remaining segments is just the marked fraction , or .

The correct answer is E.

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My solution.
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Lets say the branch is 15 m long(taking lcm of 3 and 5)
Then the markings are at 5, 10 , 15 and 3, 6 , 9 , 12 , 15
1-3 length 2
3-5 length 2
5-6 length 1
6-9 length 3
9-10 length 1
10-12 length 2
12-15 length 3

So the distinct intervals are 1, 2, 3.
there are 2 1's , 3 2's and and 2 3's. They are 3 in mumber.
If you remove the one of each
so 2 + 1 + 3 / (15) = 6 / 15 = 3/5 is the answer.

[LazyNK]

But the question is "What fraction of the original branch remains".
First, 1+2+3/15=6/15=2/5 ( not 3/5 as you write)
So fraction remaining = 1-2/5=3/5
-NK

[jnelson0612]

But the question is "What fraction of the original branch remains".
First, 1+2+3/15=6/15=2/5 ( not 3/5 as you write)
So fraction remaining = 1-2/5=3/5
-NK

Good catch, thanks!

[hiokitsutomu]

In this question, what does "one piece of every distinct length" mean?

[RonPurewal]

In this question, what does "one piece of every distinct length" mean?

You go into a place that sells pizza by the slice. You say, "I'd like one piece of every kind."
I bet you have no issues understanding that one. This is the same.

Remember, the wording of the problems is just like "normal" wording on planet earth.
They look weird largely because they're presented in the form of dense, impersonal text. However, you can always interpret them the same way you would in everyday life.