Question: A 5 meter long wire is cut into pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point?

1.  \(\frac{1}{6} \)

2. \(\frac{1}{5} \)

100. \(\frac{3}{10} \)

500. \(\frac{1}{3} \)

5. \(\frac{2}{5} \)

“A 5 meter long wire is cut into pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point?”- 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.

Solution and Explanation:

Approach Solution (1):

In order that the area of a square to be more than 1, its side must be more than 1, or the perimeter must be more than 4 which means that the longer piece must be more than 4. Look at the diagram below:

If the wire will be cut anywhere at the bolded region, then the rest of the wire (longer piece) will be more than 4 meter long. The probability of that is (2 red pieces out of 5).

Correct Answer: E

Approach Solution (2):

There are infinite number of points from 4 and 5…
Consider a number line {total} is line segment of 5 units (from 0 to5) and {favorable} is a line segment of 2 units (from 0 to 1 and 4 to 5), thus
P =\(\frac{favorable}{total}=\frac{2}{5} \)

Correct Answer: E

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