The pipe was marked in fourths and thirds.

1/4 = 3/12

1/3 = 4/12

So the pipe was market first at 3/12 intervals and then at 4/12 intervals.

Here's the pipe. - - - - - - - - - - - -

First mark it every 3/12. - - -|- - -|- - -|- - -

Now mark it every 4/12. - - -|-|- -|- -|-|- - -

Look at the pieces.

- - - = 3/12 = 1/4

- = 1/12

- - = 2/12 = 1/6

That covers all of them. 1/4, 1/12, 1/6

So the correct answer is D.

Here's a more advanced way to look at it.

Fourths are smaller than thirds. Cutting a pipe at 1/4 markings will make only pieces 1/4 or smaller. So any answer choice with 1/3 in it is eliminated.

That leaves, A and D.

The first cut is at 1/4 = 3/12 The second cut is at 1/3 = 4/12. Those cuts are 1/12 apart. So there has to be at least one 1/12 piece.

A does not include 1/12. D includes 1/12.

So it's done and the answer is D.

oquiella wrote:A straight pipe 1 yard in length was marked off off in fourths and also in thirds. If the pipe was hen 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, and 1/6, and 1/4
E. 1/12, 1/6, and 1/3

Ignore the given length of 1 yard.
The problem can be solved using any length.

Let the pipe = 12 yards.
Dividing 12 into 3rds will yield markings at 4 and 8.
Dividing 12 into 4ths will yield markings at 3, 6, and 9.

Listing the markings in order, we get:
0......3..4....6....8..9......12

There are only 3 distinct differences between markings: 1 yards, 2 yards, and 3 yards.
Phrasing these differences as fractions, we get:
1/12.
2/12 = 1/6.
3/12 = 1/4.

The correct answer is D.

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https://www.beatthegmat.com/700-question-t87924.html