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A wire is cut into three equal parts. The resulting...

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A wire is cut into three equal parts. The resulting...

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

The OA is E.

I'm confused with this PS question. Experts, any suggestion? How can I determine the minimum length? Thanks in advance.

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GMAT/MBA Expert

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

The OA is E.

I'm confused with this PS question. Experts, any suggestion? How can I determine the minimum length? Thanks in advance.
Hi LUANDATO,
Let's take a look at your question.

Suppose that the minimum length of wire be 3x.
If it is cut into three equal pieces, length of each piece will be x.

The resulting segments are then cut in 4, 6 and 8 equal parts respectively.
4 pieces will be of length x/4 each.
6 pieces will be of length x/6 each.
8 pieces will be of length x/8 each.

Since, each of the resulting segments has an integer length, therefore, x/4, x/6 and x/8 will result into integer values.
It means x is the least common multiple of 4, 6, 8.
Multiples of 4 = 4, 8, 12, 16, 20, 24, ...
Multiples of 6 = 6, 12, 18, 24, 30, ...
Multiples of 8 = 8, 16, 24, 32, ...

LCM of 4, 6 and 8 = 24
It means x = 24
The minimum length of wire = 3x = 3(24) = 72

Therefore, Option E is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
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LUANDATO wrote:
A wire is cut into three equal parts. The resulting segments are then cut in 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 can PLUG IN THE ANSWERS, which represent the minimum length of the wire.
When we plug in the correct answer, we will be able to divide the wire first into 3 equal parts and then into 4, 6, and 8 equal parts.
Since the question stem asks for the MINIMUM length, start with the smallest answer choice.

A: 24
If a 24-inch wire is divided into 3 equal parts, the length of each part = 24/3 = 8.
The value in red cannot be divided into 6 equal parts.
Eliminate A.

B: 36
If a 36-inch wire is divided into 3 equal parts, the length of each part = 36/3 = 12.
The value in red cannot be divided into 8 equal parts.
Eliminate B.

C: 48
If a 48-inch wire is divided into 3 equal parts, the length of each part = 48/3 = 16.
The value in red cannot be divided into 6 equal parts.
Eliminate C.

D: 54
If a 54-inch wire is divided into 3 equal parts, the length of each part = 54/3 = 18.
The value in red cannot be divided into 8 equal parts.
Eliminate D.

The correct answer is E.

E: 72
If a 72-inch wire is divided into 3 equal parts, the length of each part = 72/3 = 24.
Success!
The value in green can be divided into 4, 6, and 8 equal parts.

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GMAT/MBA Expert

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LUANDATO wrote:
A wire is cut into three equal parts. The resulting segments are then cut in 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

_________________

Jeffrey Miller
Head of GMAT Instruction
jeff@targettestprep.com



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