Question: 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?

1. 24
2. 36
3. 48
4. 54
5. 72

“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?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution (1):

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

Correct option: E

Approach Solution (2):

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 each wire, we want the length of each of the equal parts to be 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 * 24 = 72.

Correct option: E

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