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M14#17

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M14#17 [#permalink] New post 24 Jun 2012, 12:04
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

50% (02:36) correct 50% (02:25) wrong based on 6 sessions
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) \frac{1}{6}

B) \frac{1}{5}

C) \frac{3}{10}

D) \frac{1}{3}

E) \frac{2}{5}

Can someone please explain this problem? Also, the official explanation states: "Look at the diagram below" but the diagram is not provided. Thanks.
[Reveal] Spoiler: OA
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Re: M14#17 [#permalink] New post 24 Jun 2012, 12:08
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Below is OE with the diagram. Was not it displayed on the test?

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).

Answer: E.
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Re: M14#17 [#permalink] New post 24 Jun 2012, 12:57
Oh, that was suppose to be the diagram. I was expecting a bigger diagram. I thought they were some kind of hash marks. :lol: It it posted on the test but it is not color coded. Thanks for the explanation.
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Re: M14#17 [#permalink] New post 25 Jun 2012, 20:51
Bunuel wrote:
Below is OE with the diagram. Was not it displayed on the test?

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).

Answer: E.


Thanks Bunuel, thats very good explanation, but could you clarify onemore thing, isn't 2/5 the probability of getting area of the square which equals to 1. Since cutting on any red sides will leave us longer wire with length 4 which is not more than 1 in area but just equal.
Thanks.
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Re: M14#17 [#permalink] New post 26 Jun 2012, 00:27
Bunuel wrote:
Below is OE with the diagram. Was not it displayed on the test?

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).

Answer: E.



Hi Bunnel,

One query...

Seeing the figure how can we say that three(Black dashes) sum to length more than 4?
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Re: M14#17 [#permalink] New post 26 Jun 2012, 00:52
Expert's post
ziko wrote:
Bunuel wrote:
Below is OE with the diagram. Was not it displayed on the test?

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).

Answer: E.


Thanks Bunuel, thats very good explanation, but could you clarify onemore thing, isn't 2/5 the probability of getting area of the square which equals to 1. Since cutting on any red sides will leave us longer wire with length 4 which is not more than 1 in area but just equal.
Thanks.


kotela wrote:
Hi Bunnel,

One query...

Seeing the figure how can we say that three(Black dashes) sum to length more than 4?


I think you both do not understand one thing: each dash is 1 meter long. So, again if we cut anywhere at the red region (from 0 to 1 meter or from 4 to 5 meters) then the rest of the wire (longer piece) will be more than 4 meter long.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Manager
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Re: M14#17 [#permalink] New post 26 Jun 2012, 02:39
Bunuel wrote:
ziko wrote:
Bunuel wrote:
Below is OE with the diagram. Was not it displayed on the test?

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).

Answer: E.


Thanks Bunuel, thats very good explanation, but could you clarify onemore thing, isn't 2/5 the probability of getting area of the square which equals to 1. Since cutting on any red sides will leave us longer wire with length 4 which is not more than 1 in area but just equal.
Thanks.


kotela wrote:
Hi Bunnel,

One query...

Seeing the figure how can we say that three(Black dashes) sum to length more than 4?


I think you both do not understand one thing: each dash is 1 meter long. So, again if we cut anywhere at the red region (from 0 to 1 meter or from 4 to 5 meters) then the rest of the wire (longer piece) will be more than 4 meter long.


Got it! So basically the crucial point for me here is cutting "at" the red region, for some reason i was concentrating on cutting exactly between the dashes.
Many thanks Bunuel!
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Joined: 28 Jul 2011
Posts: 583
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Re: M14#17 [#permalink] New post 26 Jun 2012, 03:02
Bunuel wrote:
ziko wrote:
Bunuel wrote:
Below is OE with the diagram. Was not it displayed on the test?

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).

Answer: E.


Thanks Bunuel, thats very good explanation, but could you clarify onemore thing, isn't 2/5 the probability of getting area of the square which equals to 1. Since cutting on any red sides will leave us longer wire with length 4 which is not more than 1 in area but just equal.
Thanks.


kotela wrote:
Hi Bunnel,

One query...

Seeing the figure how can we say that three(Black dashes) sum to length more than 4?


I think you both do not understand one thing: each dash is 1 meter long. So, again if we cut anywhere at the red region (from 0 to 1 meter or from 4 to 5 meters) then the rest of the wire (longer piece) will be more than 4 meter long.


Many thanks Bunnel....Got It
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Re: M14#17   [#permalink] 26 Jun 2012, 03:02
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