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Director  Joined: 29 Nov 2012
Posts: 741
The three squares above share vertex A with AF = FE and AE =  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 70% (01:56) correct 30% (01:50) wrong based on 289 sessions

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Attachment: Untitled.png [ 24.89 KiB | Viewed 6371 times ]
The three squares above share vertex A with AF = FE and AE = ED. If a point X is randomly selceted from square region ABCD, what is the probability that X will be contained in the shaded region?

A. 1/16
B. 1/12
C. 1/4
D. 3/16
E. 1/3

Originally posted by fozzzy on 09 Jan 2013, 20:34.
Last edited by Bunuel on 23 Jan 2014, 05:20, edited 1 time in total.
Edited the question.
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VP  Joined: 02 Jul 2012
Posts: 1158
Location: India
Concentration: Strategy
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Re: The three squares above share vertex A with AF = FE and AE =  [#permalink]

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6
1
fozzzy wrote:
The three squares above share vertex A with AF = FE and AE = ED. If a point X is randomly selceted from square region ABCD, what is the probability that X will be contained in the shaded region?

A) 1/16
B) 1/12
c) 1/4
D) 3/16
4) 1/3

Lets say AD = 4, So, AE = 2 & AF = 1.

Area of ABCD = 16
Area of Square with side AE = 4
Area of Square with side AF = 1

Area of shaded region = 4-1 = 3

Probability = $$\frac{Area of shaded region}{Area of ABCD}$$ = $$\frac{3}{16}$$

Answer is D.
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Director  Joined: 29 Nov 2012
Posts: 741
Re: The three squares above share vertex A with AF = FE and AE =  [#permalink]

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MacFauz wrote:
fozzzy wrote:
The three squares above share vertex A with AF = FE and AE = ED. If a point X is randomly selceted from square region ABCD, what is the probability that X will be contained in the shaded region?

A) 1/16
B) 1/12
c) 1/4
D) 3/16
4) 1/3

Lets say AD = 4, So, AE = 2 & AF = 1.

Area of ABCD = 16
Area of Square with side AE = 4
Area of Square with side AF = 1

Area of shaded region = 4-1 = 3

Probability = $$\frac{Area of shaded region}{Area of ABCD}$$ = $$\frac{3}{16}$$

Answer is D.

The figure is so deceiving easy way to trick a person! Thanks for the solution!
Manager  Joined: 18 Oct 2011
Posts: 84
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Re: The three squares above share vertex A with AF = FE and AE =  [#permalink]

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Say each side of the largest square is 4. This gives a totall area of 16.
Since AF=FE and AE=ED, AF and FE must both equal 1 and ED must equal two. Based on this, the area of the 2nd smallest square is 4 and the smallest square is one...giving us an area of 3 for the shaded region.

Therefore the probability of x being in the shaded region is 3/16. D.
Intern  Joined: 08 Jan 2013
Posts: 4
Re: The three squares above share vertex A with AF = FE and AE =  [#permalink]

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1
the probability of the point to lie in shaded region is giveny by

area of the shaded region / area of the original square

To find the area of shaded region = area of the square formed by side AE - area of the square formed by side AF

If we assume that the side AD = 1 unit; then from given info we can take AF = 1/4 and AE = 1/2

Then the area of the square formed by side AE would be 1/4 and the area of the square formed by side AF would be 1/16
Therefore, area of the shaded region = 1/4 minus 1/16 = 3/16

We can take this 3/16 directly as probability because the area of the original square is 1 unit from out assumption of orginal side to be 1 unit.

thanks
Mohan
Manager  Joined: 28 Dec 2013
Posts: 68
Re: The three squares above share vertex A with AF = FE and AE =  [#permalink]

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MacFauz wrote:
fozzzy wrote:
The three squares above share vertex A with AF = FE and AE = ED. If a point X is randomly selceted from square region ABCD, what is the probability that X will be contained in the shaded region?

A) 1/16
B) 1/12
c) 1/4
D) 3/16
4) 1/3

Lets say AD = 4, So, AE = 2 & AF = 1.

Area of ABCD = 16
Area of Square with side AE = 4
Area of Square with side AF = 1

Area of shaded region = 4-1 = 3

Probability = $$\frac{Area of shaded region}{Area of ABCD}$$ = $$\frac{3}{16}$$

Answer is D.

how do we know AE = 2 and AF = 1 instead of the reverse order?
Manager  Joined: 02 Nov 2014
Posts: 185
GMAT Date: 08-04-2015
Re: The three squares above share vertex A with AF = FE and AE =  [#permalink]

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sagnik242 wrote:
MacFauz wrote:
fozzzy wrote:
The three squares above share vertex A with AF = FE and AE = ED. If a point X is randomly selceted from square region ABCD, what is the probability that X will be contained in the shaded region?

A) 1/16
B) 1/12
c) 1/4
D) 3/16
4) 1/3

Lets say AD = 4, So, AE = 2 & AF = 1.

Area of ABCD = 16
Area of Square with side AE = 4
Area of Square with side AF = 1

Area of shaded region = 4-1 = 3

Probability = $$\frac{Area of shaded region}{Area of ABCD}$$ = $$\frac{3}{16}$$

Answer is D.

how do we know AE = 2 and AF = 1 instead of the reverse order?

Hi,
A per Q, AF = FE. So, AE = 2*AF.
If we assume AF = 1, it implies AE = 2.
Hope that helps.
Senior Manager  G
Joined: 04 Aug 2010
Posts: 413
Schools: Dartmouth College
Re: The three squares above share vertex A with AF = FE and AE =  [#permalink]

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fozzzy wrote:
Attachment:
Untitled.png
The three squares above share vertex A with AF = FE and AE = ED. If a point X is randomly selceted from square region ABCD, what is the probability that X will be contained in the shaded region?

A. 1/16
B. 1/12
C. 1/4
D. 3/16
E. 1/3

Let AF=FE=1, with the result that AE=ED=2: As the figure illustrates:
shaded region = 1+1+1 = 3
ABCD = 4*4 = 16
$$\frac{shaded}{ABCD} = \frac{3}{16}$$

.
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