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
OG 2016  Q227
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 ceilidh.erickson
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Start by drawing a picture and marking off fourths and thirds:
Then, convert these to a common denominator: twelfths.
Now, measure the distance between each:
There are pieces of 3/12, 2/12, and 1/12.
Simplify: 1/4, 1/6, and 1/12
The answer is D.
Then, convert these to a common denominator: twelfths.
Now, measure the distance between each:
There are pieces of 3/12, 2/12, and 1/12.
Simplify: 1/4, 1/6, and 1/12
The answer is D.
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Since the answer choices are FRACTIONS, the problem can be solved using ANY length for the pipe.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
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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