If a continuous cable 10m long was marked off at intervals of 1/4 mete

Question

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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hr1212 · Accepted Answer

Multiple ways to attempt this =>

1. Mark all the points b/w 0 and 1, and that should give us all different size lengths, as the pattern repeats after a fixed interval. In this case it repeats after 0.5, so that too should suffice.

0, 1/5, 1/4, 2/5, 2/4, 3/5, 3/4, 4/5, 1

Unique differences are 1/5 (1/5 - 0), 1/20 (1/4 - 1/5), 3/20 (2/5 - 1/4), 1/10 (2/4 - 2/5), hence there are 4 different unique lengths.

2. Easier way could be to multiply these numbers by LCM (20) and to calculate unique adjacent number differences

0, 4, 5, 8, 10, 12, 15, 16, 20 => Unique differences are 1, 2, 3, 4

3. Can be validated from graph too.

IMO: C

bhargavhhhhhhhh · Answer

1. Intervals Given:
 - Marks at 1/4 meter: 0, 1/4, 1/2, ..., 10.
 - Marks at 1/5 meter: 0, 1/5, 2/5, ..., 10.

2. Common Interval:
 - LCM of 1/4 and 1/5 is 1/20, so marks occur every 1/20 meter.

3. Segment Lengths:
 - Possible segment lengths:
 - 1/20
 - 1/4 = 5/20
 - 1/5 = 4/20

4. Unique Segment Sizes:
 - Unique lengths are 1/20, 4/20, 5/20.

Answer: 3 unique segment sizes. (C)

ADisHere · Answer

Here in the below image, as there are only 4 lengths (5, 15, 20 and 10) So there are 4 different size length of cable Option C https://gmatclub.com/forum/download/file.php?id=83470 GMAT-Club-Forum-mu3h86dx.jpeg

Gmat750aspirant · Answer

1. Mark all points between 0 and 1. The pattern repeats after a fixed interval. In this case, it repeats every 0.5, so we get the following points:

0, 1/5, 1/4, 2/5, 2/4, 3/5, 3/4, 4/5, 1

The unique differences between consecutive points are:
1/5 (1/5 - 0)
1/20 (1/4 - 1/5)
3/20 (2/5 - 1/4)
1/10 (2/4 - 2/5)

Thus, there are 4 unique distances.

2. A simpler method is to multiply each point by the LCM (20) and find the unique differences between consecutive points:

0, 4, 5, 8, 10, 12, 15, 16, 20

The unique differences are: 1, 2, 3, 4

3. This can also be verified using a graph.

C

Whoisdmx15 · Answer

As is obvious that this pattern shall repeat after a meter.
In order to do it within 2 minutes, and to process it easier (where the divisions of string would be), we can either multiply the fractions by a LCM (i.e 20) or convert the fractions into decimals. (This lets us visualize whether 1/4 and1/5 series cuts are between 2 1/4 cuts)
Now, plot them on the timeline as attached)

Hence, 04 different lengths are there" 0.2,0.05,0.15,.1

IMO Ans C

sujoykrdatta · Answer

The actual length is irrelevant.

Assume it to be 20m
The markings are: 
1/5th: 4,8,12,16,20
1/4th: 5,10,15,20
Sort in order, the markings are at: 
4,5,8,10,12,15,16,20
So sizes of the pieces are: 
4,1,3,2,2,3,1,4

Distinct sizes: 4
 Answer C

onlymalapink · Answer

why are we only allowed to count consecutive cuts what's the logic

arushi118 · Answer

length of whole cable: 1000cm
cuts at 25cm and 20cm
---------------------------------------------
SO take from 1 to 100 cm:
we will have cuts:
0 to 20cm -- 20 (length)
20 to 25cm -- 5 (length)
25 to 40cm -- 15 (length)
40 to 50cm -- 10 (length)
50 to 60cm -- 10 (length)
60 to 75cm -- 15 (length)
75 to 80cm -- 5 (length)
80 to 100cm -- 20 (length)

it will repeat for the rest of the length of the cable
So, different size length of cable: 20cm, 5cm, 15cm, 10cm
 C is correct

yashsharma1 · Answer

See if this makes sense guys, I found it easier this way

We can take cumulative lengths for each length of cuts
So, for 1/5 length cuts in a meter, the cuts will be at 0.2, 0.4, 0.6, 0.8 and 1 meter
similarly, for 1/4 cuts in a meter, the cuts will be at 0.25, 0.50, 0.75 and 1 meter
If I combine these, the cuts will be at 0.2, 0.25, 0.4, 0.5, 0.6, 0.75, 0.8 and 1 meter. 
We can then see the gaps in each of these which would be 0.2m (diff between 0 to 0.2 and 0.8 to 1 meter cut), 0.05m (diff between 0.2 to 0.25 and 0.75 to 0.8 meter cut), 0.15m (diff between 0.25 to 0.4, 0.6 to 0.75 meter cut) and 0.10m (diff between 0.4 to 0.5, 0.5 to 0.6 meter cut). This will keep repeating in each meter.

Hence answer is 4 unique lengths

If a continuous cable 10m long was marked off at intervals of 1/4 mete

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If a continuous cable 10m long was marked off at intervals of 1/4 mete

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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