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 a rectangular coordinate system, point A has coordinates [#permalink]
20 Aug 2010, 13:30

3

This post received KUDOS

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

70% (04:19) correct
30% (03:32) wrong based on 134 sessions

In a rectangular coordinate system, point A has coordinates (d, d), where d > 0. Point A and the origin form the endpoints of a diameter of circle C. What fraction of the area of circle C lies within the first quadrant?

Re: What fraction of the area of circle C lies within ... [#permalink]
20 Aug 2010, 13:48

1

This post received KUDOS

Ok so I am typing this on my mobile with imagination... Imagine a square of side 1 and a circle circumscribed.. Qn is what is the area that is lying on the 2 bulging sides.. Area of square = 1 area of circle = pi/2

The area of 4 bulging sides = (pi/2-1) Fraction of circle area inside 1st Q= [pi/2-1/2(pi/2-1)]/pi/2 = (pi/2-pi/4+1/2)/(pi/2) = (pi/4+1/2)/(pi/2) = (pi+2)/2pi

Posted from my mobile device _________________

Consider kudos, they are good for health

Last edited by mainhoon on 20 Aug 2010, 15:05, edited 2 times in total.

Re: What fraction of the area of circle C lies within ... [#permalink]
20 Aug 2010, 14:15

3

This post received KUDOS

Expert's post

Financier wrote:

In a rectangular coordinate system, point A has coordinates (d, d), where d > 0. Point A and the origin form the endpoints of a diameter of circle C. What fraction of the area of circle C lies within the first quadrant?

Answer-choises will come later.

Look a the diagram:

Attachment:

CS.jpg [ 22.42 KiB | Viewed 4723 times ]

We have circle with radius=1 and square inscribed in it. Now imagine the base of square to be x-axis and left side of square to be y-axis. We need to find the ratio of area of a circle without the red parts to the area of whole circle.

Area of a circle is C=\pi{r^2}=\pi; Area of a square is half of the product of diagonals, as diagonal equals to 2r=2, then S=\frac{2^2}{2}=2;

Area of a circle without the red parts is C-\frac{C-S}{2}=\pi-\frac{\pi-2}{2}=\frac{\pi+2}{2};

Ratio of the are of this region to area of a circle is \frac{\frac{\pi+2}{2}}{\pi}=\frac{\pi+2}{2\pi}.

Re: What fraction of the area of circle C lies within ... [#permalink]
23 Oct 2010, 12:33

Let us assume A to be (1,1).Then, distance from origin = sqrt 2 = Diagonal of square = Diameter of circle.

Area of square = 1 sq units and Area of circle = Pi r^2 = Pi (sqrt 2 / 2)^2 = Pi / 2

Area of 4 bulging sides = (Pi/2) - 1 = (Pi - 2) / 2 and Area of 2 bulging side = (Pi - 2) / 4.

Therefore, required fraction = Area of 2 bulging side / Area of circle = [(Pi - 2) / 4] / (Pi/2) = Pi -2 / 2Pi.

But answer posted by Bunuel is : Pi + 2 / 2Pi and I take his explainations as absolute. Since I got a different answer....please explain where I am wrong.

Re: What fraction of the area of circle C lies within ... [#permalink]
19 Apr 2012, 21:08

mainhoon wrote:

Ok so I am typing this on my mobile with imagination... Imagine a square of side 1 and a circle circumscribed.. Qn is what is the area that is lying on the 2 bulging sides.. Area of square = 1 area of circle = pi/2

The area of 4 bulging sides = (pi/2-1) Fraction of circle area inside 1st Q= [pi/2-1/2(pi/2-1)]/pi/2 = (pi/2-pi/4+1/2)/(pi/2) = (pi/4+1/2)/(pi/2) = (pi+2)/2pi

Posted from my mobile device

Great work!!...Appreciate the stratgy. _________________

KUDOS-ing does'nt cost you anything, but might just make someone's day!!!

Re: In a rectangular coordinate system, point A has coordinates [#permalink]
08 Aug 2012, 07:57

Hi, Cant we do this by calculating the area of the sector and then the area of the circle??? Pls help me understand! _________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

Re: In a rectangular coordinate system, point A has coordinates [#permalink]
08 Aug 2012, 16:41

es we can do it by taking any value for (d,d) and calculating the area deducting the sector. Take (d,d) as 2,2. the dia meter becomes 2 root 2 and radius root2 so area of circle = 2pie area of 2 sectors= 2*(90/360)*2 pie = pie But have to add another half of square = 1/2 * 4 = 2 So area in 1st quadrant = 2pie-pie+2= pie+2 and area of circle = 2pie So ratio= (2+pie)/2pie _________________

Re: What fraction of the area of circle C lies within ... [#permalink]
23 Jan 2013, 09:15

Bunuel wrote:

Financier wrote:

In a rectangular coordinate system, point A has coordinates (d, d), where d > 0. Point A and the origin form the endpoints of a diameter of circle C. What fraction of the area of circle C lies within the first quadrant?

Answer-choises will come later.

Look a the diagram:

Attachment:

CS.jpg

We have circle with radius=1 and square inscribed in it. Now imagine the base of square to be x-axis and left side of square to be y-axis. We need to find the ratio of area of a circle without the red parts to the area of whole circle.

Area of a circle is C=\pi{r^2}=\pi; Area of a square is half of the product of diagonals, as diagonal equals to 2r=2, then S=\frac{2^2}{2}=2;

Area of a circle without the red parts is C-\frac{C-S}{2}=\pi-\frac{\pi-2}{2}=\frac{\pi+2}{2};

Ratio of the are of this region to area of a circle is \frac{\frac{\pi+2}{2}}{\pi}=\frac{\pi+2}{2\pi}.

Answer: D.

Hope it's clear.

Hi,

Area of a circle without the red parts is C-\frac{C-S}{2}=\pi-\frac{\pi-2}{2}=\frac{\pi+2}{2};

is already describing the circle's portion, which is available in 1st Q. why we have again check for the ratio b/w this and circle again.I got this doubt since question has asked us to find the fraction of the area of circle C lies within the first quadrant.

Re: What fraction of the area of circle C lies within ... [#permalink]
23 Jan 2013, 13:19

1

This post was BOOKMARKED

FTG wrote:

Bunuel wrote:

Financier wrote:

In a rectangular coordinate system, point A has coordinates (d, d), where d > 0. Point A and the origin form the endpoints of a diameter of circle C. What fraction of the area of circle C lies within the first quadrant?

Answer-choises will come later.

Look a the diagram:

Attachment:

CS.jpg

We have circle with radius=1 and square inscribed in it. Now imagine the base of square to be x-axis and left side of square to be y-axis. We need to find the ratio of area of a circle without the red parts to the area of whole circle.

Area of a circle is C=\pi{r^2}=\pi; Area of a square is half of the product of diagonals, as diagonal equals to 2r=2, then S=\frac{2^2}{2}=2;

Area of a circle without the red parts is C-\frac{C-S}{2}=\pi-\frac{\pi-2}{2}=\frac{\pi+2}{2};

Ratio of the are of this region to area of a circle is \frac{\frac{\pi+2}{2}}{\pi}=\frac{\pi+2}{2\pi}.

Answer: D.

Hope it's clear.

Hi,

Area of a circle without the red parts is C-\frac{C-S}{2}=\pi-\frac{\pi-2}{2}=\frac{\pi+2}{2};

is already describing the circle's portion, which is available in 1st Q. why we have again check for the ratio b/w this and circle again.I got this doubt since question has asked us to find the fraction of the area of circle C lies within the first quadrant.

Kindly help me understand ..

The question asks for "fraction" or "proportion" of the circle. (e.g. say 1/2 or 3/5th of circle lies in the first quadrant) Hence you need to take the ratio of Area (in 1st quadrant) to Total area to find the fraction. _________________

Re: What fraction of the area of circle C lies within ... [#permalink]
04 Feb 2013, 08:37

Bunuel wrote:

Financier wrote:

In a rectangular coordinate system, point A has coordinates (d, d), where d > 0. Point A and the origin form the endpoints of a diameter of circle C. What fraction of the area of circle C lies within the first quadrant?

Answer-choises will come later.

Look a the diagram:

Attachment:

CS.jpg

We have circle with radius=1 and square inscribed in it. Now imagine the base of square to be x-axis and left side of square to be y-axis. We need to find the ratio of area of a circle without the red parts to the area of whole circle.

Area of a circle is C=\pi{r^2}=\pi; Area of a square is half of the product of diagonals, as diagonal equals to 2r=2, then S=\frac{2^2}{2}=2;

Area of a circle without the red parts is C-\frac{C-S}{2}=\pi-\frac{\pi-2}{2}=\frac{\pi+2}{2};

Ratio of the are of this region to area of a circle is \frac{\frac{\pi+2}{2}}{\pi}=\frac{\pi+2}{2\pi}.

Answer: D.

Hope it's clear.

Quote:

Area of a square is half of the product of diagonals, as diagonal equals to 2r=2, then S=\frac{2^2}{2}=2;

is this because you are taking into account the portion of the square which doesnt touch the red parts of the circle? Since area of Square is A = a^2 ?

Re: What fraction of the area of circle C lies within ... [#permalink]
05 Feb 2013, 02:40

Expert's post

pharm wrote:

Bunuel wrote:

Financier wrote:

In a rectangular coordinate system, point A has coordinates (d, d), where d > 0. Point A and the origin form the endpoints of a diameter of circle C. What fraction of the area of circle C lies within the first quadrant?

Answer-choises will come later.

Look a the diagram:

Attachment:

CS.jpg

We have circle with radius=1 and square inscribed in it. Now imagine the base of square to be x-axis and left side of square to be y-axis. We need to find the ratio of area of a circle without the red parts to the area of whole circle.

Area of a circle is C=\pi{r^2}=\pi; Area of a square is half of the product of diagonals, as diagonal equals to 2r=2, then S=\frac{2^2}{2}=2;

Area of a circle without the red parts is C-\frac{C-S}{2}=\pi-\frac{\pi-2}{2}=\frac{\pi+2}{2};

Ratio of the are of this region to area of a circle is \frac{\frac{\pi+2}{2}}{\pi}=\frac{\pi+2}{2\pi}.

Answer: D.

Hope it's clear.

Quote:

Area of a square is half of the product of diagonals, as diagonal equals to 2r=2, then S=\frac{2^2}{2}=2;

is this because you are taking into account the portion of the square which doesnt touch the red parts of the circle? Since area of Square is A = a^2 ?

If I understand correctly you are asking about the area of a square: area_{square}=side^2=\frac{diagonal^2}{2}. This is a general formula for the area of any square.

Re: In a rectangular coordinate system, point A has coordinates [#permalink]
05 Feb 2013, 04:55

Expert's post

pharm wrote:

Yea, thank you cleared things up

Forgot to mention that the area of a rhombus is also equals to half of the product of diagonals: area_{rhombus}=\frac{d_1*d_2}{2}, where d_1 and d_2 are the lengths of the diagonals (or bh, where b is the length of the base and h is the altitude). _________________

Re: In a rectangular coordinate system, point A has coordinates [#permalink]
22 Aug 2014, 14:54

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. _________________