A 5-Meter-Long Wire is Cut into Two Pieces. If the Longer Piece GMAT Problem Solving

Question: A 5-meter-long wire is cut into two 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. 1/6
2. 1/5
3. 3/10
4. 1/3
5. 2/5

Answer: E

Solution and Explanation:

Approach Solution 1:

A 5-meter wire is divided into two parts. What is the likelihood that, if the original wire was severed at any time, the longer section was utilized to create a square's perimeter and that the square's area would be more than 1?

In order for 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. This means that the longer piece must be more than 4. Look at the diagram below:

– – – – –

The remainder of the wire (longer piece), if the wire is severed anywhere in the bolded area, will be longer than 4 metres. That has a 2/5 chance of happening (2 red pieces out of 5).

E is the correct answer.

Approach Solution 2:

Two segments of a 5-meter wire are separated. How likely is it that if the original wire was ever broken, the longer piece would have been used to make a square's perimeter and its area would have been more than one?

Fundamental formula: probability = (desired results)/ (possible outcomes)

The longer of the two wires' potential outcomes is = 5-2.5 = 2.5.
Results that are more than 4 = 5-4=1 are desired for the longer wire.

The probability will therefore be = 1/2.5 = 2/5.

The right response is E.

Approach Solution 3:

A 5-meter wire is divided into two parts. What is the likelihood that, if the original wire was severed at any time, the longer section was utilized to create a square's perimeter and that the square's area would be more than 1?

5-meter wire length

A longer piece of wire can be obtained at 2.6, 2.7, 2.8,... 5.0 --> 25 ways if the markings are set up so that each metre has 10 subdivisions.

Square Area > 1 when Perimeter > 4.

when the wire is severed at points > 4, the perimeter 4.0 m —> 4.1, 4.2, .... 5.0 —> 10 ways

Probability equals 10/25, or 2/5.

E is the correct answer.

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