Simple explanation needed: Arithmetic:

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Divya Ann Chacko: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Mon Nov 25, 2013 8:30 am

Simple explanation needed: Arithmetic:

by Divya Ann Chacko » Tue Dec 03, 2013 9:36 am

A straight pipe 1 yard 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

Given answer is option D

I didnt understand the question. Also how they arrived to the answer. Can it be explained, please?

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Source: Beat The GMAT — Problem Solving | Tue Dec 03, 2013 9:36 am

Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 am; Thanked: 25 times; Followed by:1 members

by Mathsbuddy » Tue Dec 03, 2013 9:51 am

Quarters and thirds have a common denominator of 3 * 4 = 12

Therefore replace with equivalent fractions:

1/4 = 3/12, 2/4 = 6/12, 3/4 = 9/12
1/3 = 4/12, 2/3 = 8/12

Put into order of size:
3/12, 4/12, 6/12, 8/12, 9/12

In other words, the twelfths are arranged:
0, 3, 4, 6, 8, 9, 12 (from end to end)

Each is a cutting point (including the pre-cut ends)

Between each cut we have twelfths of:

3 - 0 = 3
4 - 3 = 1
6 - 4 = 2
8 - 6 = 2
9 - 8 = 1
12 - 9 = 3

Ignoring duplicates, the sizes are therefore:

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

Hence answer d) 1/12, 1/6 and 1/4

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Divya Ann Chacko: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Mon Nov 25, 2013 8:30 am

by Divya Ann Chacko » Tue Dec 03, 2013 9:54 am

What is an equivalent fraction? can you please explain it?

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Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 am; Thanked: 25 times; Followed by:1 members

by Mathsbuddy » Tue Dec 03, 2013 9:57 am

Divya Ann Chacko wrote:What is an equivalent fraction? can you please explain it?

Sure.
I think it's easier if you "see" it!
Look at https://www.mathsisfun.com/equivalent_fractions.html

I'll be off-line until tomorrow, so I hope this helps. Sorry, I have to rush off. Good luck!