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A 7 meter long wire is cut into two pieces at an arbitrary point. The

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KarunMendiratta
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A 7 meter long wire is cut into two pieces at an arbitrary point. The [#permalink] New post   11 Aug 2021, 08:35
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A 7 meter long wire is cut into two pieces at an arbitrary point. The longer piece is then used to form a square.

Quantity A
Quantity B
Probability that the area of the square will be more than 1 \(m^2\)
\(\frac{4}{5}\)


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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Re: A 7 meter long wire is cut into two pieces at an arbitrary point. The [#permalink] New post   12 Aug 2021, 05:04
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Explanation:

Note: Longer piece has to be greater than 3.5m

Let the increment in the pieces be 0.5m

So, total outcomes could be 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0 i.e. 7 outcomes

Now, if the area has to be greater than 1\(m^2\), each side should be greater than 1. Therefore, perimeter of the square has to be greater than 4.

So, favorable outcomes could be 4.5, 5.0, 5.5, 6.0, 6.5, 7.0 i.e. 6 outcomes

Required probability = \(\frac{6}{7}\)

Col. A: 0.85
Col. B: 0.80

Hence, option A
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Re: A 7 meter long wire is cut into two pieces at an arbitrary point. The [#permalink] New post   11 Aug 2021, 10:11
is it d.
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Re: A 7 meter long wire is cut into two pieces at an arbitrary point. The [#permalink] New post   11 Aug 2021, 21:27
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Longer piece is always greater than 3.5 . So obviously area will be greater than 3.5^2
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Re: A 7 meter long wire is cut into two pieces at an arbitrary point. The [#permalink] New post   11 Aug 2021, 22:00
I am little bit confused here. It does not mention that length must be integer. then, If the piece of length 6 and 1 possible. If not, only possible value for length is 4 and 3.
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Re: A 7 meter long wire is cut into two pieces at an arbitrary point. The [#permalink] New post   11 Aug 2021, 22:01
venkyappu19981999 wrote:
Longer piece is always greater than 3.5 . So obviously area will be greater than 3.5^2


And the probability will thus be greater than 0.80???
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Re: A 7 meter long wire is cut into two pieces at an arbitrary point. The [#permalink] New post   11 Aug 2021, 23:34
COolguy101 wrote:
I am little bit confused here. It does not mention that length must be integer. then, If the piece of length 6 and 1 possible. If not, only possible value for length is 4 and 3.

due same reason I choosed D.
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Re: A 7 meter long wire is cut into two pieces at an arbitrary point. The [#permalink] New post   12 Aug 2021, 04:28
venkyappu19981999 wrote:
Longer piece is always greater than 3.5 . So obviously area will be greater than 3.5^2


Sir, the longer piece will not be the side of square
Hint: The perimeter has to be greater than 4 sq. units
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Re: A 7 meter long wire is cut into two pieces at an arbitrary point. The [#permalink] New post   13 Aug 2021, 18:39
KarunMendiratta wrote:
Explanation:

Note: Longer piece has to be greater than 3.5m

Let the increment in the pieces be 0.5m

So, total outcomes could be 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0 i.e. 7 outcomes

Now, if the area has to be greater than 1\(m^2\), each side should be greater than 1. Therefore, perimeter of the square has to be greater than 4.

So, favorable outcomes could be 4.5, 5.0, 5.5, 6.0, 6.5, 7.0 i.e. 6 outcomes

Required probability = \(\frac{6}{7}\)

Sir, I did not understand, Is there any easy way to deal with?

Col. A: 0.85
Col. B: 0.80

Hence, option A
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Re: A 7 meter long wire is cut into two pieces at an arbitrary point. The [#permalink] New post   17 Oct 2023, 08:11
KarunMendiratta wrote:
Explanation:

Note: Longer piece has to be greater than 3.5m

Let the increment in the pieces be 0.5m

So, total outcomes could be 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0 i.e. 7 outcomes

Now, if the area has to be greater than 1\(m^2\), each side should be greater than 1. Therefore, perimeter of the square has to be greater than 4.

So, favorable outcomes could be 4.5, 5.0, 5.5, 6.0, 6.5, 7.0 i.e. 6 outcomes

Required probability = \(\frac{6}{7}\)

Col. A: 0.85
Col. B: 0.80

Hence, option A


How do you know that it should be greater that 3.5 and that increments need to be in 0.5 ???? PLEASE HELP. I AM VERY SCARED NOW
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Re: A 7 meter long wire is cut into two pieces at an arbitrary point. The [#permalink] New post   17 Oct 2023, 10:49
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Hint: The perimeter has to be greater than 4 sq. units

Thatìs why he says that should be more than 3.5

However,. I agree also with someone above about that the length could be also NOT an integer.

As for the increment of 0.5 is just a way to see what is going on with the question.

trial and error
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Re: A 7 meter long wire is cut into two pieces at an arbitrary point. The [#permalink]
17 Oct 2023, 10:49
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