Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 05:58

### GMAT Club Daily Prep

#### 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

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

# M23-27

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56306

### Show Tags

16 Sep 2014, 01:19
1
3
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:25) correct 31% (01:23) wrong based on 152 sessions

### HideShow timer Statistics

The center of the circle is at point $$(0, 6)$$. If the distance between the two points where the circle intersects the x-axis is 16, what is the area of the circle?

A. $$36\pi$$
B. $$45\pi$$
C. $$64\pi$$
D. $$81\pi$$
E. $$100\pi$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 56306

### Show Tags

16 Sep 2014, 01:19
Official Solution:

The center of the circle is at point $$(0, 6)$$. If the distance between the two points where the circle intersects the x-axis is 16, what is the area of the circle?

A. $$36\pi$$
B. $$45\pi$$
C. $$64\pi$$
D. $$81\pi$$
E. $$100\pi$$

The radius of the circle $$= \sqrt{6^2 + 8^2} = 10$$. The area $$= \pi10^2 = 100\pi$$.

_________________
Intern
Joined: 21 May 2013
Posts: 7

### Show Tags

26 Dec 2014, 03:25
Or even more simple:

Identify that you have a 3-4-5 (6-8-10) triangle and without calculation you know that the hypothenuse is 10 => radius is 10.
Manager
Joined: 01 Aug 2014
Posts: 54
Schools: Rotman '17 (A)
GMAT 1: 710 Q44 V42

### Show Tags

28 Jan 2016, 11:10
I took the wrong approach with this question, would someone kindly clarify?

I had done a quick sketch of 0,6 on a graph and assumed that since the distance between the first point and where x meets the number line (x, 0) then the hypotenuse would be 16, and the radius would therefore be 16.

Where am I going wrong? I recognize that a 6-8-10 triangle can be formed from the side with a value of 6 however how does length 16 factor into this? Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 56306

### Show Tags

28 Jan 2016, 23:38
2
Anonamy wrote:
I took the wrong approach with this question, would someone kindly clarify?

I had done a quick sketch of 0,6 on a graph and assumed that since the distance between the first point and where x meets the number line (x, 0) then the hypotenuse would be 16, and the radius would therefore be 16.

Where am I going wrong? I recognize that a 6-8-10 triangle can be formed from the side with a value of 6 however how does length 16 factor into this? Thanks

The center of the circle is on y-axis, so it's symmetric around it. We know that the the distance between the two points where the circle intersects the x-axis is 16, hence half of it (8 units) must be to the left of 0 and the remaining half (another 8 units) to the right of 0.

As you can see the radius of the circle is a hypotenuse of a right triangle with the sides equal to 6 and 16/2=8 (6-8-10 right triangle), so radius=hypotenuse=10. The area is $$\pi{r^2}=100\pi$$.

Attachment:
Circle.png

>> !!!

You do not have the required permissions to view the files attached to this post.

_________________
Senior Manager
Joined: 31 Mar 2016
Posts: 376
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

### Show Tags

25 Jul 2016, 06:54
I think this is a high-quality question and I agree with explanation. Wow. This is a 700 level question certainly not 600 as classified by you Bunuel. Anyway terrific question in my view! Great work!
Senior Manager
Joined: 08 Jun 2015
Posts: 421
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33

### Show Tags

22 Mar 2018, 10:13
+1 for option E. Draw the graph , the answer will stand out almost immediately !
_________________
" The few , the fearless "
Manager
Joined: 31 Jan 2018
Posts: 69
GMAT 1: 700 Q46 V40

### Show Tags

22 Mar 2018, 13:12
100pi
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2943

### Show Tags

26 Mar 2018, 10:59

Solution:

Given:

• Centre of the circle is at (6,0)

• The distance between points where the circle intersects the x-axis = 16 units

Working out:

We need to find out the area of the circle.

To solve this problem, let us first draw a proper diagram.

The distance AB is 16 units (given in the question)

Since the diagram is symmetrical, AC=CB= AC/2 = 8 units.

OC = 6 units

Thus, AO (Radius of the circle) = $$\sqrt{( 6^2 + 8^2)}$$ = $$\sqrt{100}$$ = 10 units

Hence the area of the square = $$pie * 10^2 = 100 pie$$

_________________
Re: M23-27   [#permalink] 26 Mar 2018, 10:59
Display posts from previous: Sort by

# M23-27

Moderators: chetan2u, Bunuel