Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

The three squares above share vertex A with AF = FE and AE = [#permalink]

Show Tags

09 Jan 2013, 20:34

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

67% (02:20) correct
33% (01:12) wrong based on 141 sessions

HideShow timer Statistics

Attachment:

Untitled.png [ 24.89 KiB | Viewed 2425 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?

Re: The three squares above share vertex A with AF = FE and AE = [#permalink]

Show Tags

09 Jan 2013, 21:37

4

This post received KUDOS

1

This post was BOOKMARKED

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. _________________

Did you find this post helpful?... Please let me know through the Kudos button.

Re: The three squares above share vertex A with AF = FE and AE = [#permalink]

Show Tags

10 Jan 2013, 18:56

1

This post received KUDOS

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.

Re: The three squares above share vertex A with AF = FE and AE = [#permalink]

Show Tags

09 Jan 2013, 21:42

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! _________________

Re: The three squares above share vertex A with AF = FE and AE = [#permalink]

Show Tags

10 Jan 2013, 08:19

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.

Re: The three squares above share vertex A with AF = FE and AE = [#permalink]

Show Tags

23 Jan 2014, 05:05

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: The three squares above share vertex A with AF = FE and AE = [#permalink]

Show Tags

04 Jul 2015, 06:34

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: The three squares above share vertex A with AF = FE and AE = [#permalink]

Show Tags

27 Nov 2015, 11:25

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?

Re: The three squares above share vertex A with AF = FE and AE = [#permalink]

Show Tags

27 Nov 2015, 11:39

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.

gmatclubot

Re: The three squares above share vertex A with AF = FE and AE =
[#permalink]
27 Nov 2015, 11:39

http://blog.ryandumlao.com/wp-content/uploads/2016/05/IMG_20130807_232118.jpg The GMAT is the biggest point of worry for most aspiring applicants, and with good reason. It’s another standardized test when most of us...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...