A straight pipe 1 yard in length was marked off in fourths

Question

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

(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

Bunuel · Accepted Answer

Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4. In this case the branch would be cut at 3, 4 , 6, 8 , and 9 meters (in black are given fourths of the length and in red thirds of the length). Distinct lengths would be: 3=3/12= 1/4 , 4-3=1= 1/12 and 6-4=2=2/12= 1/6 meters long pieces. Answer: D. Similar question to practice: on-the-number-line-above-the-segment-from-0-to-1-has-been-104204.html kim-finds-a-1-meter-tree-branch-and-marks-it-off-in-thirds-140038.html if-the-successive-tick-marks-shown-on-the-number-line-above-144053.html Hope it helps.

PareshGmat · Answer

Refer diagram below: length.png LCM of 3 & 4 = 12, marking the lengths accordingly Lengths possible are \frac{3}{12}, \frac{1}{12}, \frac{2}{12} = \frac{1}{4}, \frac{1}{12}, \frac{1}{6} Answer = D

JeffTargetTestPrep · Answer

This problem is best solved by setting up a diagram to represent the markings. We are given that we are marking the pipe into 3rds and 4ths. So we will have:

1/3, 2/3, 3/3, and ¼, 2/4, ¾, 4/4

However, for these “markings” to be more meaningful, we should create a common denominator. Because the denominators are 3 and 4, we know that the common denominator is 12. Converting each fraction, we have:

4/12, 8/12, 12/12 = 1, and 3/12, 6/12, 9/12, 12/12 = 1

Putting these in order we have:

3/12, 4/12, 6/12, 8/12, 9/12, 1

We now label this on a diagram:

https://i.imgur.com/K3R7RTl.png

We are then asked, 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?

To determine this, we need to calculate the difference between each consecutive pair of markings. This is represented in another diagram below.

https://i.imgur.com/UUzLUzu.png

1) 3/12 – 0 = 3/12 = ¼

2) 4/12 – 3/12 = 1/12

3) 6/12 – 4/12 = 2/12 = 1/6

4) 8/12 – 6/12 = 2/12 = 1/6

5) 9/12 – 8/12 = 1/12

6) 1 – 9/12 = 3/12 = ¼

Thus, the different lengths are 1/12, 1/6, and ¼.

The answer is D.

maibhihun · Answer

Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:

Here 4th : 0/4, 1/4, 2/4, 3/4, 4/4
and 3rd : 0/3, 1/3, 2/3, 3/3

Now with understood common denominator 12 write the numbers : for 4th : 0,3,6,9,12 and for 3rd : 0,4,8,12

Now comine : 0,3,4,6,8,9,12

Now find the cut with denominator 12 (Substracrt adjacent terms : 3/12, 1/12, 2/12, 1/12,3/12 i.e. 1/4, 1/12 and 1/6 after removing duplicates.

harishbiyani · Answer

Hi,

Request you could explain the answer in more detail? I did not understand how the branch would be cut at 3,4,6,8,9.

since there are two markings, there would be three distinct pieces of the branch right? 1/4th part, 1/12th part   and i cannot understand about how the third part is 1/6th?

Bunuel · Answer

Imagine that we have 12-meter long pipe.

Cut in fourths means that it's cut at 1/4th, at 2/4th and at 3/4th. Thus at 3, 6, and 9 meters.
Cut in thirds means that it's cut at 1/3rd, and at 2/3rd Thus at 4 and 8 meters.

So, it would be cut at  3,  4 , 6,  8 , and 9  meters.

Does this make sense?

In my post above there are similar questions to practice. Please go through them.

sagnik2422 · Answer

Now with understood common denominator 12 write the numbers : for 4th : 0,3,6,9,12 and for 3rd : 0,4,8,12 ( Where is 0,3,6,9,12) and 0,4,8,12 coming from for four and 3 it seems like it should be reverse to me, obviously i am mistaken, but why is this done like this?

Bunuel · Answer

Imagine that we have 12-meter long pipe.

Cut in fourths means that it's cut at 1/4th, at 2/4th and at 3/4th. Thus at 3, 6, and 9 meters.
Cut in thirds means that it's cut at 1/3rd, and at 2/3rd Thus at 4 and 8 meters.

So, it would be cut at  3,  4 , 6,  8 , and 9  meters.

Does this make sense?

In my post above there are similar questions to practice. Please go through them.

pacifist85 · Answer

I don't think you need to calculate anything here, unless I found the correct answer in random. This was the process I followed:

1) I drew a straight line for the pipe.
2) I marked the 1/4ths. This means I marked it in 3 places, as you will see in the drawing below (|).
3) I marked the 1/3rds. This means I marked it in 2 places, as you will see in the drawing below (!).

|_______|__!_____|__!_____|_______|

So, now we see the thirds and the fourths. What you see it that the "whole" pieces you see are of 3 different lenghts.
The 1/4 is seen in the begining and the end.
There is no whole 1/3 anywhere. But, there are 2 other lengths dividing the fourths: a smaller one and a larger one, marked by the !.

In other words, we need 3 different lengths:
One will be the 1/4
None will be 1/3
There will be 2 other lengths.

Only D satisfies this observation, so  ANS D .

Bunuel · Answer

Problem Solving:

https://gmatclub.com/forum/on-the-numbe ... 16629.html GMAT Prep (Focus)
https://gmatclub.com/forum/on-a-laborat ... 24877.html GMAT Prep (Focus)
https://gmatclub.com/forum/the-tick-mar ... 25298.html GMAT Prep (Focus)
https://gmatclub.com/forum/if-the-tick- ... 08185.html GMAT Prep
https://gmatclub.com/forum/on-the-numbe ... 08085.html GMAT Prep
https://gmatclub.com/forum/on-the-numbe ... 04204.html Official Guide
https://gmatclub.com/forum/a-straight-p ... 45031.html Official Guide
https://gmatclub.com/forum/on-the-numbe ... 98106.html GMAT Club Tests
https://gmatclub.com/forum/if-the-tick- ... 63234.html
https://gmatclub.com/forum/in-the-numbe ... 54299.html
https://gmatclub.com/forum/on-the-numbe ... 91631.html
https://gmatclub.com/forum/marks-are-eq ... 44534.html
https://gmatclub.com/forum/kim-finds-a- ... 40038.html
https://gmatclub.com/forum/on-the-numbe ... 26136.html

Data Sufficiency:
https://gmatclub.com/forum/if-the-succe ... 44053.html Official Guide
https://gmatclub.com/forum/if-a-b-c-and ... 20097.html Official Guide
https://gmatclub.com/forum/if-the-tick- ... 04050.html
https://gmatclub.com/forum/if-the-tick- ... 49455.html
https://gmatclub.com/forum/on-the-numbe ... 72416.html

Hope it helps.

egmat · Answer

This is a classic GMAT problem that tests your ability to work with fractions and visualize overlapping marking systems. Let's tackle this step-by-step together.

Understanding What We're Dealing With

Think of this pipe like a ruler that's 1 yard long. We need to mark it in two different ways:
- In fourths: marks at  \frac{1}{4} ,  \frac{1}{2} ,  \frac{3}{4} 
- In thirds: marks at  \frac{1}{3} ,  \frac{2}{3}

Then we cut at  every single mark  we made. Let's find all the different piece lengths.

Step 1: Find All Cut Points

Here's what you need to see - we have marks from both systems on the same pipe:
From fourths:  0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1 
From thirds:  0, \frac{1}{3}, \frac{2}{3}, 1

Now, let's put these in order. To compare fractions like  \frac{1}{4}  and  \frac{1}{3} , I'll convert to twelfths:
-  \frac{1}{4} = \frac{3}{12} 
-  \frac{1}{3} = \frac{4}{12} 
-  \frac{1}{2} = \frac{6}{12} 
-  \frac{2}{3} = \frac{8}{12} 
-  \frac{3}{4} = \frac{9}{12}

So our cut points in order are:  0, \frac{1}{4}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, 1

Step 2: Calculate Piece Lengths

Notice how we need the distance between consecutive cuts:
- From 0 to  \frac{1}{4} : Length =  \frac{1}{4} 
- From  \frac{1}{4}  to  \frac{1}{3} : Length =  \frac{4}{12} - \frac{3}{12} = \frac{1}{12} 
- From  \frac{1}{3}  to  \frac{1}{2} : Length =  \frac{6}{12} - \frac{4}{12} = \frac{2}{12} = \frac{1}{6} 
- From  \frac{1}{2}  to  \frac{2}{3} : Length =  \frac{8}{12} - \frac{6}{12} = \frac{1}{6} 
- From  \frac{2}{3}  to  \frac{3}{4} : Length =  \frac{1}{12} 
- From  \frac{3}{4}  to 1: Length =  \frac{1}{4}

Step 3: Identify Unique Lengths

Let's think about this - we have pieces of lengths:  \frac{1}{4}, \frac{1}{12}, \frac{1}{6}, \frac{1}{6}, \frac{1}{12}, \frac{1}{4}

The  different  lengths are:  \frac{1}{12}, \frac{1}{6}, \frac{1}{4}

Answer: D

You can check out the  step-by-step solution on Neuron by e-GMAT  to master the systematic approach for handling overlapping fraction systems. The complete solution reveals a powerful framework that works for all marking and cutting problems, plus shows you how to spot similar patterns instantly. You can also explore other GMAT official questions with detailed solutions on Neuron for structured practice  here .

A straight pipe 1 yard in length was marked off in fourths

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A straight pipe 1 yard in length was marked off in fourths

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