Problem Solving

Decorative ribbon is cut into three equal parts. The resulting segments are then cut into 4, 6 and 8 equal parts, respectively. If each of the resulting pieces has an integer length, what is the minimum length of the ribbon?
A. 24
B. 36
C. 48
D. 54
E. 72


OA E

sanju09 wrote:Decorative ribbon is cut into three equal parts. The resulting segments are then cut into 4, 6 and 8 equal parts, respectively. If each of the resulting pieces has an integer length, what is the minimum length of the ribbon?
A. 24
B. 36
C. 48
D. 54
E. 72


OA E

4y=x
6z=x
8p=x
y/z=3/2
y/p=2/1
y=3
z=2
p=6

4y+6z+8p=Lengh
Min Length =72

dtweah provides a great algebraic explanation, but like a lot of GMAT questions we can also just reason it out and avoid (most of) the math.

We know that each of our 3 sections are equal and that each one must be divisible by 4, 6 and 8 (since each piece has integer length).

The lowest common multiple of 4, 6 and 8 is 24. Therefore, the smallest possible length of each third is 24.

24*3 = 72... choose (E).