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.

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:

In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
07 Feb 2013, 14:30

Expert's post

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

81% (01:57) correct
19% (01:19) wrong based on 68 sessions

Attachment:

2-to-1 rectangle with circle.JPG [ 19.83 KiB | Viewed 1138 times ]

In the diagram above, the sides of rectangle ABCD have a ratio AB:BC = 1:2, and the circle is tangent to three sides of the rectangle. If a point is chosen at random inside the rectangle, what is the probability that it is not inside the circle?

Re: 2-to-1 rectangle with circle [#permalink]
07 Feb 2013, 23:15

1

This post received KUDOS

mikemcgarry wrote:

Attachment:

2-to-1 rectangle with circle.JPG

In the diagram above, the sides of rectangle ABCD have a ratio AB:BC = 1:2, and the circle is tangent to three sides of the rectangle. If a point is chosen at random inside the rectangle, what is the probability that it is not inside the circle? (A) \frac{4-{\pi}}{4} (B) \frac{4+{\pi}}{4} (C) \frac{4+{\pi}}{8} (D) \frac{8-{\pi}}{8} (E) \frac{8+{\pi}}{8} For a discussion of Geometric Probability, as well as a complete explanation of this particular question, see: http://magoosh.com/gmat/2013/geometric- ... -the-gmat/ Mike

Let the smaller side of square = 2x Larger side will be = 4x Radius of the circle will be = x Area of the Square = 8x2 Area of the Circle = \pix2

the probability that the point is inside the circle = Area of the Circle/ Area of the Square = (\pix2)/ (8x2) = \pi/8

the probability that the point is not inside the circle = 1 - the probability that the point is inside the circle = 1- \pi/8

Answer D

Hope it helps _________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
08 Feb 2013, 02:00

1

This post received KUDOS

mikemcgarry wrote:

Attachment:

2-to-1 rectangle with circle.JPG

In the diagram above, the sides of rectangle ABCD have a ratio AB:BC = 1:2, and the circle is tangent to three sides of the rectangle. If a point is chosen at random inside the rectangle, what is the probability that it is not inside the circle?

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
08 Feb 2013, 08:08

Assume the sides of the rectangle to be 2 and 4. Diameter of the circle=AB=2 Radius of the circle=1 Area of circle= {\pi} Area of the rectangle = 2*4=8 Area of the rectangle outside circle = 8-{\pi} So, probability= 8-{\pi}/8

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
09 Feb 2013, 17:58

Let us assume the sides of the rectangle be 1 and 2, so the area of the rectangle is 2 which implies that the circle is inscribed within a square whose area is 1.

Area of circle inscribed within a square is \frac{pi}{4} times the area of square = \frac{pi}{4}

Probability of point not inside the circle = 1 - probability of point inside the circle = 1 - (pi/4)/2 = 1 - \frac{pi}{8} = \frac{(8-pi)}{8}

Re: In the diagram above, the sides of rectangle ABCD have a rat [#permalink]
11 Feb 2013, 11:17

Expert's post

nave81 wrote:

p.s how does one type the symbol of pi?

Dear nave81 ---

It's funny. I was wondering this same thing, and I had to quote a response of Bunuel in which he used the {\pi} symbol to see what it looked like in the html text.

Basically, you type {\pi} ----- (open curvy brackets)(backstroke)("pi")(close curvy brackets) ---- and then highlight that in the "math" delimiters ---- the m button, under the bold button in the rtf bar at the top of the editing window, does this. All math symbols need to be within the "math" delimiters.

Does this make sense?

Mike _________________

Mike McGarry Magoosh Test Prep

gmatclubot

Re: In the diagram above, the sides of rectangle ABCD have a rat
[#permalink]
11 Feb 2013, 11:17