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Decorative ribbon is cut

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by sanju09 » Sat May 09, 2009 5:39 am
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
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Re: Decorative ribbon is cut

by dtweah » Sat May 09, 2009 5:58 am
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
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by Stuart@KaplanGMAT » Sat May 09, 2009 9:43 am
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).
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