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# If a continuous cable 10m long was marked off at intervals

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Manager
Joined: 02 Jun 2011
Posts: 126
If a continuous cable 10m long was marked off at intervals  [#permalink]

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05 Jun 2012, 06:31
9
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:57) correct 36% (02:00) wrong based on 241 sessions

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If a continuous cable 10m long was marked off at intervals of 1/4 meter and also 1/5 meter, and then if the cable were cut at each mark, how many different size length of cable would result?

A. 1
B. 6
C. 4
D. 5
E. 2
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Re: if a continous cable  [#permalink]

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05 Jun 2012, 06:42
2
2
Draw a line segment
Mark the ends as 0 and 10m
Now divide it in one fifths and mark the divisions(similar to mile stones in the highway)
So right now the markings are at
2m, 4m, 6m, 8m and 10m
Do the same for one fourths
So in this case the markings are at
2.5m, 5m, 7.5m,
Now see the individual line segments that are formed
1. From 0m -2m
2. From 2m-2.5m
3. From 2.5m-4m
4. From 4m-5m
5. From 5m-6m
6. From 6m-7.5m
7. From 7.5m-8m
8. From 8m-10m
Hence there are 2 line segments for each of the following lengths
2m, 0.5m, 1.5m, 1m
I.e C
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Re: If a continuous cable 10m long was marked off at intervals  [#permalink]

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05 Jun 2012, 08:33
2
In this particular example length (10 meter) is just extraneous information.

So now, considering marks for 1/4 mt. and 1/5 mt. So we can see marks at following lengths:

1/5, 1/4, 2/5, 2/4, 3/5, 3/4, 4/5, 1......

so distance between adjacent marks :

1/20, 3/20, 2/20, 2/20, 3/20, 1/5 =>

1/20, 3/20, 1/10, 1/5

So there would be pieces of 4 different size lengths.

so distance between adjacent marks :

1/20, 3/20, 2/20, 2/20, 3/20, 1/5 =>

1/20, 3/20, 1/10, 1/5

So there would be pieces of 4 different size lengths.
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Re: If a continuous cable 10m long was marked off at intervals  [#permalink]

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24 Apr 2018, 10:38
kashishh wrote:
If a continuous cable 10m long was marked off at intervals of 1/4 meter and also 1/5 meter, and then if the cable were cut at each mark, how many different size length of cable would result?

A. 1
B. 6
C. 4
D. 5
E. 2

Let’s get a common denominator of 20.

For the intervals of 1/4 meter we have:

5/20, 10/20, 15/20 and 20/20

For the intervals of 1/5 meter we have:

4/20, 8/20, 12/20, 16/20, and 20/20

Thus, we see we could have lengths of:

5/20 - 4/20 = 1/20,

8/20 - 5/20 = 3/20,

10/20 - 8/20 = 2/20, and

20/20 - 16/20 = 4/20.

Thus we have 4 different size lengths.

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If a continuous cable 10m long was marked off at intervals  [#permalink]

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30 Apr 2018, 12:15
kashishh wrote:
If a continuous cable 10m long was marked off at intervals of 1/4 meter and also 1/5 meter, and then if the cable were cut at each mark, how many different size length of cable would result?

A. 1
B. 6
C. 4
D. 5
E. 2

Attachment:

segments.png [ 8.82 KiB | Viewed 444 times ]

Sketching is a quick way to solve.
Well under a minute with a sketch . . .

Draw a line

Divide into fourths: 0---2.5---5---7.5---10

And then into fifths:0---2---4---6---8---10

Write the lengths: 2 | 0.5 | 1.5 | 1 | 1, 0.5, 1.5, 2

Second half mirrors first half (segment lengths are identical)

There are 4 different lengths (circled in figure)

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If a continuous cable 10m long was marked off at intervals &nbs [#permalink] 30 Apr 2018, 12:15
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