Problem Solving

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 of 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

D

Sana I think it is 1/12,1/6 and 1/4 not 112,16 and 14

|---1/4---|-1/12-|--1/6--|--1/6--|-1/12-|---1/4---|
0--------1/4------1/3-----1/2-----2/3-----3/4---------1

1/4, 1/3-1/4 = 1/12, 1/2-1/3=1/6

sana.noor wrote: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 of the different lengths of the pieces, in fractions of a yard?

a)1/6 and 1/4 only
b)1/4 and 13 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

D

Hi Sana,

This problem will be easy to visualise if you consider the length of the wire to be 12yards rather than 1 yard. Now the result will be same because we will be dividing by the same factor.
So suppose you have a 12 yard wire. There will be marking at 4,8 and 12. Also we will have markings at 3,6 and 9. Now if we break it into part this will happen.

From starting point till mark of 3 we will have a piece of 3 yards. So this piece is equal to 3/12=1/4 fraction.
From 3 yards mark till the next mark which is 4 yards we have 1 yard piece. So this piece will be 1/12 ( now you can easily eliminate A B and C at this point)
From 4 yard mark the next mark is 6 yards. So the piece size will be 2 yards. So the fraction is 2/12=1/6.

Now if you check the rest pieces you will get the same size pieces( for understanding next mark will be at 8 yards and it is 2 yards away from 6 yards so the size will be 2/12=1/6) so all the other pieces will be the same as we already got.

So the final answer is D

sana.noor wrote: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 of 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

Note : 1/4 < 1/3 < 2/4 < 2/3 < 3/4 < 1
or 25% < 33.33% < 50% < 66.66% < 75%< 100%



[spoiler]Correct answer: D[/spoiler]

Regards,
Vivek

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

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:
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.

Check here for a similar problem:

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