I got this question wrong in an
MGMAT CAT.
However, I was able to solve it later during review.
My approach was to draw a number line and mark off the thirds and the fifths, as shown below:
Attachment:
nl.jpg [ 8.46 KiB | Viewed 1321 times ]
I used the decimal equivalents to help me arrange the fractions on the number-line.
Now, it is tempting to calculate the differences of the decimal values. The challenge with this approach is that fractions like 1/3, 2/3, etc. might lead to rounding errors later.
In summary, I think that Bunuel's approach using LCM is the the perfect way to solve such a problem.
The same number line, now on a scale of [0-15]:
Attachment:
nl2.jpg [ 4.94 KiB | Viewed 1328 times ]
Difference={
3, 2, 1, 3, 1, 2, 3}
We need to take away the 1st piece of each distinct length.
Fraction of original branch left=\(\frac{3+1+2+3}{15}=\frac{9}{15}=\frac{3}{5}\)