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# A 5 meter long wire is cut into two pieces. If the longer

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Math Expert
Joined: 02 Sep 2009
Posts: 47946
Re: A 5 meter long wire is cut into two pieces. If the longer  [#permalink]

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25 Sep 2016, 02:55
yezz wrote:
I would very much appreciate if someone can point out the flaw in my logic

the line is cut into 2 pieces ....x , 5-x

assuming x is the larger piece then x>2.5....... ( the larger piece)

side of square = x/4 , area of square = x^2/16 , question is to test x^2/16>1

we get ............-4................4.............. the inequality is true in the ranges x<-4 and x>4 but we have a restriction that x>2.5 thus x>4

thus 4<x<5 , thus probability = (5-4)/5 = 1/5 ............Bunuel where am i going wrong if you plz.

What if 5-x is larger piece and not x. In this case you'd have (5 - x)^2/16 > 1 giving x < 1.
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Re: A 5 meter long wire is cut into two pieces. If the longer  [#permalink]

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19 May 2017, 00:58
Bunuel wrote:
SravnaTestPrep wrote:
Bunuel wrote:

OK, let me ask you this: what is the probability that the wire will be cut so that we get pieces of exactly 4m and 1m (so at 1m or at 4m)?

What I'm saying is that the probability that the length of a longer piece will be more than 4 OR more than or equal to 4 is the same and equal to 2/5.

I think the answer 2/5 is flawed. Let us take five points 1, 2, 3, 4 and 5. For the longer wire to be more than or equal to 4m, 2 cases are there, it has to be cut at 1m or before OR 4m or after.

Let us take the first case. For example if it is cut at 1m, the longer wire would be 4m. Assume that each 1m is divided into cms. So there are 99 points out of a total of 500 points when the longer wire can be more than 4 m. for example if it is cut at 99th cm the longer wire would be 401 cm or > 4m. and so on. So there are totally 100 points including the exact 1m point out of a total of 500 points. So the probability that the longer wire is equal to or more than 4m is 100/500=1/5. The other case is wire cut at 4m and above. Each case has a probability of 1/5 so that the overall probability is 2/5.

The above is also equivalent to saying that the shorter wire is <= 1m. That is the probability is 2/5 when the longer wire is 4m and the shorter wire is 1m and say when the longer wire is 4.01 m and the shorter wire is 0.99m and so on . But saying equal to or more than 4m is not equivalent to saying less than 1m but only equivalent to saying less than or equal to 1m.

So when we have the shorter wire to be less than 1m, we have to consider only the cases > 4m. When it has to be more than 4m, the probability will be less than the above or less than 2/5.

The correct answer is E (2/5).

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?

A. 1/6
B. 1/5
C. 3/10
D. 1/3
E. 2/5

In order 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 red region then the rest of the wire (longer piece) will be more than 4 meter long. The probability of that is 2/5 (2 red pieces out of 5).

Why do we consider the 1st and 2d red region as two separate instances. the rope doesn't have two distinct ends right? Cut at region 1 or region 2 it gives the same result.
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Re: A 5 meter long wire is cut into two pieces. If the longer  [#permalink]

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19 May 2017, 01:15
goforgmat wrote:

Why do we consider the 1st and 2d red region as two separate instances. the rope doesn't have two distinct ends right? Cut at region 1 or region 2 it gives the same result.

The rope does have two ends. We can get more than 4 meter long piece if we cut the rope in any of the red regions.
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Re: A 5 meter long wire is cut into two pieces. If the longer  [#permalink]

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06 Jul 2017, 02:01
MisterEko wrote:
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?

A) 1/6
B) 1/5
C) 3/10
D) 1/3
E) 2/5

OA says it is 2/5 because:

The area of the square will be more than 1 if and only if the longer piece of the wire is longer than 4. To produce such a result, the cutting point has to be either on the first meter of the wire or on its last meter. The probability of this is 2/5 .

I have a question. Since area of the square has to be more than 1, its sides have to be more than 1. If its sides are more than 1, its perimeter will be more than 4. In order for this to happen, a piece larger than 4 meters has to be cut. The smallest piece need would be 4 meters and 1 centimeter (or millimeter for that matter). While I agree that the chance of wire being cut on any of the first 1 meters of it is 2/5, don't we need to calculate the probability of it being cut (at least) at 4 meters and 1 centimeter (or mm)? If so, the probability that it will get cut within first 99 cm is 2*99/500, which comes out to 99/250. This is close to 2/5 yes, but isn't this more correct way to look at it?

What I'm wondering is that is it a GMAT question? Bunuel please answer
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Re: A 5 meter long wire is cut into two pieces. If the longer  [#permalink]

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06 Jul 2017, 02:05
ShashankDave wrote:
MisterEko wrote:
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?

A) 1/6
B) 1/5
C) 3/10
D) 1/3
E) 2/5

OA says it is 2/5 because:

The area of the square will be more than 1 if and only if the longer piece of the wire is longer than 4. To produce such a result, the cutting point has to be either on the first meter of the wire or on its last meter. The probability of this is 2/5 .

I have a question. Since area of the square has to be more than 1, its sides have to be more than 1. If its sides are more than 1, its perimeter will be more than 4. In order for this to happen, a piece larger than 4 meters has to be cut. The smallest piece need would be 4 meters and 1 centimeter (or millimeter for that matter). While I agree that the chance of wire being cut on any of the first 1 meters of it is 2/5, don't we need to calculate the probability of it being cut (at least) at 4 meters and 1 centimeter (or mm)? If so, the probability that it will get cut within first 99 cm is 2*99/500, which comes out to 99/250. This is close to 2/5 yes, but isn't this more correct way to look at it?

What I'm wondering is that is it a GMAT question? Bunuel please answer

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I don't see why not.
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Re: A 5 meter long wire is cut into two pieces. If the longer  [#permalink]

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06 Jul 2017, 02:17
MisterEko wrote:
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?

A) 1/6
B) 1/5
C) 3/10
D) 1/3
E) 2/5

OA says it is 2/5 because:

The area of the square will be more than 1 if and only if the longer piece of the wire is longer than 4. To produce such a result, the cutting point has to be either on the first meter of the wire or on its last meter. The probability of this is 2/5 .

I have a question. Since area of the square has to be more than 1, its sides have to be more than 1. If its sides are more than 1, its perimeter will be more than 4. In order for this to happen, a piece larger than 4 meters has to be cut. The smallest piece need would be 4 meters and 1 centimeter (or millimeter for that matter). While I agree that the chance of wire being cut on any of the first 1 meters of it is 2/5, don't we need to calculate the probability of it being cut (at least) at 4 meters and 1 centimeter (or mm)? If so, the probability that it will get cut within first 99 cm is 2*99/500, which comes out to 99/250. This is close to 2/5 yes, but isn't this more correct way to look at it?

Area of the square > 1.
so, Side >1.
so, perimeter > 4.

Now we need to think of cutting the wire such that the larger piece of wire has a length > 1.
So, lets put a wire of 5 m length and measure it from left.
Required condition is possible only if it is cut before 1 m mark or after 4 m mark.
It should not be cut between 1 m mark to 4 m mark
It can be represented as below.
______1______2______3______4_______5

So, required probability = 2/5.

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Re: A 5 meter long wire is cut into two pieces. If the longer  [#permalink]

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05 Dec 2017, 22:49
Senthil1981 wrote:
MisterEko wrote:
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?

A) 1/6
B) 1/5
C) 3/10
D) 1/3
E) 2/5

Let the place where the rope is cut be $$x$$ and it's used to form a square with $$x$$ as perimeter and hence side is $$\frac{x}{4}$$ and Area =$$\frac{x^2}{4}$$
The area should be more than 1 so $$x^2/4 > 1$$ , so $$x^2 > 4$$ giving $$x > 2$$.
Out the places where it can be cut, 1,2,3,4 , 3 and 4 are above 2, so $$\frac{2}{5}$$ Answer is E

If the side is x/4, the area will be ($$x^2$$)/16 and not ($$x^2$$)/4
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Re: A 5 meter long wire is cut into two pieces. If the longer  [#permalink]

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22 Jan 2018, 16:26
Hi All,

This question is vaguely worded in spots, but I've offered an explanation that matches the 'intent' of the question. There's an aspect to this question that many Test Takers would miss: regardless of where on the wire the 'cut' is made, the 'longer' piece is the one that's used to make the square. Thus, unless you cut the wire exactly in the middle, there are will always be two versions of each measure.

For example...
if you cut the wire at the 1m "mark", you'll have a 1m piece and a 4m piece
if you cut the wire at the 4m "mark", you'll also have a 1m piece and a 4m piece

Since area of a square is (side)^2, for the area to be GREATER than 1 m^2, the side lengths have to be GREATER than 1. By extension, this means that the perimeter would have to be GREATER than 4. Thus, any cut that produces a longer piece that is greater than 4m will satisfy what this question is asking for...

Cutting LESS than 1m will do it.
Cutting MORE than 4m will also do it.

That's approximately 2m of a 5m wire... 2/5

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Re: A 5 meter long wire is cut into two pieces. If the longer  [#permalink]

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22 Jan 2018, 20:04
[quote="MisterEko"]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?

A) 1/6
B) 1/5
C) 3/10
D) 1/3
E) 2/5

Good Question. Let the two parts cut be a & b. Now, $$a + b =5.$$ Given, square is formed with greater side (Suppose a). So,$$a = 4s$$ (S is the side of each square).

The question is asking for $$S^2 > 1$$ or $$a^2/16 > 1$$ which means $$4<a<5$$. Now, this wire can be cut from 1 to 2 or from 4 to 5, hence two possibilities.. i.e. $$2/5$$
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Re: A 5 meter long wire is cut into two pieces. If the longer &nbs [#permalink] 22 Jan 2018, 20:04

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