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A wire is cut into three equal parts. The resulting segments are then

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Bunuel
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A wire is cut into three equal parts. The resulting segments are then [#permalink] New post   04 Dec 2015, 00:48
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A wire 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 segments has an integer length, what is the minimum length of the wire?

A. 24
B. 36
C. 48
D. 54
E. 72
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A wire is cut into three equal parts. The resulting segments are then [#permalink] New post   04 Dec 2015, 02:05
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4=2^2
6=2*3
8=2^3

LCM of 4,6 and 8 = 2^3 * 3 = 24
Since each of three equal parts will be of length 24 each.
Minimum length of original wire = 24*3= 72

Answer E
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Re: A wire is cut into three equal parts. The resulting segments are then [#permalink] New post   09 Feb 2018, 11:06
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Bunuel wrote:
A wire 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 segments has an integer length, what is the minimum length of the wire?

A. 24
B. 36
C. 48
D. 54
E. 72


We see that each of the 3 equal parts must be a multiple of 4, 6 and 8. Since we want the minimum length of the wire, we want the length of each of the equal parts to be the least common multiple (LCM) of 4, 6 and 8. The LCM of 4, 6 and 8 is 24. Thus the minimum length of each of the 3 equal parts is 24 and the minimum length of the original wire is 3 x 24 = 72.

Answer: E
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A wire is cut into three equal parts. The resulting segments are then [#permalink] New post   10 Feb 2018, 01:01
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Bunuel wrote:
A wire 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 segments has an integer length, what is the minimum length of the wire?

A. 24
B. 36
C. 48
D. 54
E. 72


Let \(l\) be the length of the wire cut in 3 equal parts = \(a\)
\(a = \frac{l}{3}\). Also, we have \(a = 4x = 6y = 8z\)
\(l = 12x = 18y = 24z\)
Now, only when \(l = 72\), all x,y,z will be integer.
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Re: A wire is cut into three equal parts. The resulting segments are then [#permalink] New post   22 Nov 2023, 08:17
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Re: A wire is cut into three equal parts. The resulting segments are then [#permalink]
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