cut into segments

[mehrasa]

A piece of string is marked in segments of one-fourth the lenght of the setring and also in segments of one-third the lenght of the string. If the string is then cut at each mark. which of the following expresses all the different lenghts of the bits of string, in fractions, of the original lenght?

A) 1/12 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

I solved like this ...........1/4.....1/3.............1
the 1st segment is 1/4
the 2nd segment 1/3-1/4=1/12
the 3rd segment is 2/3but it seems I made a mistake to calculate for the 3rd part.. could u plz tell me where I did wrong?
[spoiler]OA: D[/spoiler]

[GMATGuruNY]

A piece of string is marked in segments of one-fourth the lenght of the setring and also in segments of one-third the lenght of the string. If the string is then cut at each mark. which of the following expresses all the different lenghts of the bits of string, in fractions, of the original lenght?

A) 1/12 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

I solved like this ...........1/4.....1/3.............1
the 1st segment is 1/4
the 2nd segment 1/3-1/4=1/12
the 3rd segment is 2/3but it seems I made a mistake to calculate for the 3rd part.. could u plz tell me where I did wrong?
[spoiler]OA: D[/spoiler]

Let the length = 12.

Dividing 12 into fourths will yield markings at 3,6,and 9.
Dividing 12 into thirds will yield markings at 4 and 8.
The result:

0...3..4...6...8..9...12.

Unique lengths are 1, 2 and 3, yielding the following fractions:
1/12
2/12 = 1/6
3/12 = 1/4.

The correct answer is D.

[mehrasa]

[/quote]Let the length = 12.

Dividing 12 into fourths will yield markings at 3,6,and 9.
Dividing 12 into thirds will yield markings at 4 and 8.
The result:

0...3..4...6...8..9...12.

Unique lengths are 1, 2 and 3, yielding the following fractions:
1/12
2/12 = 1/6
3/12 = 1/4.

The correct answer is D.[/quote]



you mean that always when it is about cutting into three segments we have to consider, 1, 2, and 3
AND the differences is that LCM we choose according to different numbers??

for exp) if the segments were 1/6, 1/8
we can say, LCM=24
we consider, 1, 2, and 3 ==> 1/24, 2/24=1/12 and 3/24=1/8??/

[GMATGuruNY]

you mean that always when it is about cutting into three segments we have to consider, 1, 2, and 3
AND the differences is that LCM we choose according to different numbers??

for exp) if the segments were 1/6, 1/8
we can say, LCM=24
we consider, 1, 2, and 3 ==> 1/24, 2/24=1/12 and 3/24=1/8??/

Let the length = 24.

Dividing 24 into eighths will yield markings at 3, 6, 9, 12, 15, 18, and 21.
Dividing 24 into sixths will yield markings at 4, 8, 12, 16, and 20.
The result:

0....3..4...6...8..9...12...15..16...18...20..21....24.

Unique lengths are 1, 2 and 3, yielding the following fractions:
1/24
2/24 = 1/12
3/24 = 1/8.