So when we mark at intervals of thirds, the marks are at the positions 1/3 and 2/3 from the starting point.
And when we mark at intervals of fifths, the marks are at the positions 1/5, 2/5, 3/5, 4/5 from the starting point.

To make the comparison easier, we can write 1/3 and 2/3 as 5/15 and 10/15 respectively.
Similarly, we can write 1/5, 2/5, 3/5, 4/5 as 3/15, 6/15, 9/15 and 12/15 respectively.

So, now if we look at all the above 6 marks one by one from the starting point, the marks are at the following positions:
3/15 from start, 5/15 from start, 6/15, 9/15, 10/15 and 12/15 respectively. Cutting at exactly these 6 marks, we will get 7 pieces of wire which will be of following lengths (from the start):

3/15, 2/15, 1/15, 3/15, 1/15, 2/15 and 3/15 respectively. The largest length as we can see is that of 3/15 or 1/5. Hence C answer

C

Lets say the wire length is 1000mm (1m). it is cut at every 1/5th i.e 200m, 400mm, 600mm, 800mm and again at every 1/3rd i.e 333.33mm and 666.66mm. Clearly the longest distance of the cut wire is 0 to 200mm and 800mm to 1000mm. which is 200/1000 = 1/5. Hence C

So our 5ths are marked at 1/5, 2/5, 3/5 and 4/5.

Our 3rds are marked at 1/3 and 2/3.

If we use a common denominator of 15 our 5ths are marked at:

3/15, 6/15, 9/15, 12/15

And our 3rds at:

5/15, 10/15

So the largest segment 3/15 = 1/5 (occurred between the 1/5 mark and one end of the wire,between the 4/5 mark and the other end of the wire, or between the 2/5 mark and 3/5 mark).

Answer: C
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I was not able to solve this.. Bunuel's soln seems most elegant and easy to understand for me! What i still can't wrap my head around is that why this question seems so hard!! is it just me?

Hi Krish

Have you looked at this solution:

https://gmatclub.com/forum/a-one-meter- ... l#p2001263

The above solution makes it easy I guess.

I was not able to solve this.. Bunuel's soln seems most elegant and easy to understand for me! What i still can't wrap my head around is that why this question seems so hard!! is it just me? [/quote]


Hi Krish

Have you looked at this solution:

https://gmatclub.com/forum/a-one-meter- ... l#p2001263

The above solution makes it easy I guess.[/quote]

Yes, it does. thank you. quants solution always looks super easy.. i just couldn't visualize the question and was taken aback by the wording.

Visualizing the scenario makes the problem easier.

Imagine a 15-meter long wire. It is marked at 5 meters interval (1/3 of 15)

But the wire is also marked at 3 meters interval (1/5 of 15)

If you draw it properly, you will see the largest segment is 3 meters (1/5 of the wire's length).

Option: C