GMAT Math

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

The pipe is of lenght 1 yard
It is marked off in 1/4 and 1/3 parts
If there are 3 and 4 involved and it is being subdivided best approach is to take the length at 12units
This 12 equal units = 1 yard
Imagine Pipe marked 1 to 12.
Mark at the fourths i.e 1--------------3 --------------6------------9-----------------12
Mark it the thirds i.e 1------------------4-------------------8----------------------12
Biggest Part will be between 1 to 3 or 3/12 = 1/4
Smallest Part will be between 3 to 4 or 1/12
Only D qualifies. For 1/6 the Part has to be 2 units the one between 6 to 8

a video from khan's academy
https://video.answers.com/learn-for-the- ... 2-99168419

at 6min 40 seconds.
talks about symmetry from half way point....makes sense!!

HI! That link doesn't work anymore. Are there any tricks to solving these kinds of problems quickly? Thanks!

If we mark at thirds, we've got 1/3 and 2/3.

If we mark at fourths, we've got 1/4, 2/4, and 3/4.

When we cut the pipe, our pieces will be

0 to 1/4

1/4 to 1/3

1/3 to 2/4

etc.

Those first three have lengths (1/4 - 0), (1/3 - 1/4), and (1/2 - 1/3), or 1/4, 1/6, and 1/12, so we're done: the answer must be D.