First imagine a line with the following cuts:

---1/5---1/3----2/5----3/5----2/3-----4/5-----

Easiest way to find the lengths of those pieces is to find a common denominator. In this case, 15 will do. So let's redraw above like so:

---3/15---5/15----6/15----9/15----10/15-----12/15-----

Longest piece is the one from 6/15 to 9/15. 9/15 - 6/15 = 3/15 = 1/5. Answer is C.

A one meter long wire is to be marked for cutting at intervals of fifths and thirds. How long is the largest segment of the wire if the wire is cut at the marked intervals? (Source: BellCurves)

A) 1/15

B) 2/15

C) 1/5

D) 4/15

E) 9/15

There is a quick way to do this if you see a couple of things.

The first thing you need to see is that the longest you can have is a 1/5 length, because the wire is getting cut into fifths. So all the answers greater than 1/5 are out. Eliminate D and E.

Now the question is is there ever an entire 1/5.

The next thing you need to see is that 1/5 < 1/3. So the first cut will be at 1/5 and the first 1/3 cut will be past that. So there will be at least one 1/5 length.

So 1/5 is the answer and the problem is done.

Choose C.

Note that this question is virtually identical to #226 from the OG:

A straight pipe 1 yard in length was marked off in
fourths and also in thirds. If the pipe was then cut into
separate pieces at each of these markings, which of
the following gives all the different lengths of the
pieces, in fractions of a yard?

(A)1/6 and 1/4 only

(B)1/4 and 1/3 only

(C)1/6 ,1/4 and 1/3

(D)1/12 ,1/6, and 1/4

(E)1/12,1/6, and 1/3

OA D

DavidG@VeritasPrep wrote:Note that this question is virtually identical to #226 from the OG:

A straight pipe 1 yard in length was marked off in
fourths and also in thirds. If the pipe was then cut into
separate pieces at each of these markings, which of
the following gives all the different lengths of the
pieces, in fractions of a yard?

(A)1/6 and 1/4 only

(B)1/4 and 1/3 only

(C)1/6 ,1/4 and 1/3

(D)1/12 ,1/6, and 1/4

(E)1/12,1/6, and 1/3

This one can be done in a way similar to the quick way that works for the other one.

1/4 is less than 1/3. So 1/4 works and anything greater, such as 1/3, does not. Eliminate B, C and E.

A and D remain.

1/4 = 3/12 1/3 = 4/12. So they are 1/12 apart.

A does not include 1/12. So A is out.

Only choice left is D. Click it, and on to the next question.

Wow! That really helps!
Thanks so much Marty and David!!