Problem Solving

Gmat_mission 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

The length of the cable can be ANY VALUE.
To make the math easier, let the length of the cable = the product of the two denominators = 4*5 = 20 meters.

When the cable is divided into 4ths, markings are yielded at 5, 10, and 15:
0.................5.................10.................15.................20

When the cable is divided into 5th, markings are yielded at 4, 8, 12, and 16:
0.............4.............8.............12.............16.............20

The resulting cable looks as follows:
0............4..5........8.......10..12.........15..16..........20

When the cable is cut at each marking, the following distinct lengths are yielded:
4 meters (0 to 4 and 16 to 20)
1 meter (4 to 5 and 15 to 16)
3 meters (5 to 8 and 12 to 15)
2 meters (8 to 10 and 10 to 12)

The correct answer is C.