Roland2rule 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
OA is E
pls, I enjoin an expert to give the practical approach to solve this question. Thanks
Markings of the thirds: 1/3, 2/3 and 3/3
Markings of the fifths: 1/5, 2/5, 3/5, 4/5 and 5/5
They may look like this. For the sale of understanding, assume that the tree is of 15-meter length, so markings are as per the diagram given below.
---|--|-|---|-|--|---
To compare the lengths, let's make the denominators of the marking equal to 15 (= LCM of 3 and 5).
Thus, the marking are:
Markings of the thirds: 3/15, 10/15 and 15/15
Markings of the fifths: 3/15, 6/15, 9/15, 12/15 and 15/15;
Collectively, the marking are: 3/15, 5/15, 6/15, 9/15, 10/15, 12/15, and 15/15
Districts sizes are:
3/15; 5/15 - 3/15 =
2/15; 6/15 - 5/15 =
1/15
Sum of the sizes = 3/15 + 2/15 + 1/15 = 6/15
Length of the leftover branch = 1 - 6/15 = 9/15 = 3/5
The correct answer:
E
The district pieces are:
---(1)|--(2)|-(3)|---|-|--|---
Hope this helps!
-Jay
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