GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Dec 2018, 09:04

Close

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
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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • 10 Keys to nail DS and CR questions

     December 17, 2018

     December 17, 2018

     06:00 PM PST

     07:00 PM PST

    Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong.
  • R1 Admission Decisions: Estimated Decision Timelines and Chat Links for Major BSchools

     December 17, 2018

     December 17, 2018

     10:00 PM PST

     11:00 PM PST

    From Dec 5th onward, American programs will start releasing R1 decisions. Chat Rooms: We have also assigned chat rooms for every school so that applicants can stay in touch and exchange information/update during decision period.

If DB=2, AC=12, and X is the center of the circle shown as the above f

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6656
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
If DB=2, AC=12, and X is the center of the circle shown as the above f  [#permalink]

Show Tags

New post 16 Mar 2017, 00:32
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

72% (02:14) correct 28% (02:32) wrong based on 81 sessions

HideShow timer Statistics

Attachment:
geometry.png
geometry.png [ 3.58 KiB | Viewed 1447 times ]


If DB=2, AC=12, and X is the center of the circle shown as the above figure, what is the area of the circle?

A. \(20π\)
B. \(80π\)
C. \(100π\)
D. \(120π\)
E. \(160π\)

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Senior Manager
Senior Manager
User avatar
G
Joined: 19 Apr 2016
Posts: 274
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
Re: If DB=2, AC=12, and X is the center of the circle shown as the above f  [#permalink]

Show Tags

New post 16 Mar 2017, 00:52
1
1
MathRevolution wrote:
Attachment:
geometry.png


If DB=2, AC=12, and X is the center of the circle shown as the above figure, what is the area of the circle?

A. \(20π\)
B. \(80π\)
C. \(100π\)
D. \(120π\)
E. \(160π\)


let XC = r (radius), so XD = r - 2

\(r^2 = (r-2)^2 + 6^2\)

\(r^2 = r^2 - 4r + 4 + 36\)

4r = 40

r = 10

Area = pi * r * r = pi*10*10 = 100pi

Hence option C is correct
Hit Kudos if you liked it 8-)
Intern
Intern
avatar
B
Joined: 08 Sep 2016
Posts: 35
Location: Georgia
Concentration: Finance, International Business
GPA: 3.75
WE: Analyst (Investment Banking)
Re: If DB=2, AC=12, and X is the center of the circle shown as the above f  [#permalink]

Show Tags

New post 16 Mar 2017, 04:03
0akshay0 wrote:
MathRevolution wrote:
Attachment:
geometry.png


If DB=2, AC=12, and X is the center of the circle shown as the above figure, what is the area of the circle?

A. \(20π\)
B. \(80π\)
C. \(100π\)
D. \(120π\)
E. \(160π\)


let XC = r (radius), so XD = r - 2

\(r^2 = (r-2)^2 + 6^2\)

\(r^2 = r^2 - 4r + 4 + 36\)

4r = 40

r = 10

Area = pi * r * r = pi*10*10 = 100pi

Hence option C is correct
Hit Kudos if you liked it 8-)



can you explain why lines are perpendicular?
Manager
Manager
avatar
S
Joined: 17 Apr 2016
Posts: 89
Re: If DB=2, AC=12, and X is the center of the circle shown as the above f  [#permalink]

Show Tags

New post 16 Mar 2017, 08:54
0akshay0 wrote:
MathRevolution wrote:
Attachment:
geometry.png


If DB=2, AC=12, and X is the center of the circle shown as the above figure, what is the area of the circle?

A. \(20π\)
B. \(80π\)
C. \(100π\)
D. \(120π\)
E. \(160π\)


let XC = r (radius), so XD = r - 2

\(r^2 = (r-2)^2 + 6^2\)

\(r^2 = r^2 - 4r + 4 + 36\)

4r = 40

r = 10

Area = pi * r * r = pi*10*10 = 100pi

Hence option C is correct
Hit Kudos if you liked it 8-)


Hi 0akshay0

Can you explain how did you assume AC parallel to XB.
Director
Director
User avatar
S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 515
Location: India
Premium Member
Re: If DB=2, AC=12, and X is the center of the circle shown as the above f  [#permalink]

Show Tags

New post 17 Mar 2017, 02:05
radius = XA = XB = XC= r
XD = XB-BD = r-2
DA = AC/2 = 12/2 = 6
applying pythagoras theorem in triangle xad we get
r^2 = (r-2)^2 + 36

r^2 = r^2 - 4r +4 +36
r = 10

area = pi *10*10 = 100pi
_________________

GMAT Mentors
Image

Intern
Intern
avatar
B
Joined: 08 Sep 2016
Posts: 35
Location: Georgia
Concentration: Finance, International Business
GPA: 3.75
WE: Analyst (Investment Banking)
Re: If DB=2, AC=12, and X is the center of the circle shown as the above f  [#permalink]

Show Tags

New post 17 Mar 2017, 02:19
ByjusGMATapp wrote:
radius = XA = XB = XC= r
XD = XB-BD = r-2
DA = AC/2 = 12/2 = 6
applying pythagoras theorem in triangle xad we get
r^2 = (r-2)^2 + 36

r^2 = r^2 - 4r +4 +36
r = 10

area = pi *10*10 = 100pi


how do you know that DA =AC/2 ?
Manager
Manager
avatar
S
Joined: 03 Jan 2016
Posts: 59
Location: India
WE: Engineering (Energy and Utilities)
GMAT ToolKit User
Re: If DB=2, AC=12, and X is the center of the circle shown as the above f  [#permalink]

Show Tags

New post 18 Mar 2017, 10:00
Any Perpendicular Drawn from the Center of the circle to a Chord always bisects the Chord.

So AD=DC=AC/2.

Hope this Helps!!!!!!!!!!


Regards
G V V S Narayana Raju


Give +1 Kudos if u like :-D
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6656
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If DB=2, AC=12, and X is the center of the circle shown as the above f  [#permalink]

Show Tags

New post 19 Mar 2017, 17:06
Attachment:
23.png
23.png [ 5.03 KiB | Viewed 1137 times ]


You get the figure shown above, and according to the Pythagorean Theorem, you get \(r^2=(r-2)^2+6^2=r^2-4r+4+36\), and if you get rid of \(r^2\) on both sides and simplify the equation, from 4r=40, you get r=10. Thus, it becomes the area of the circle, which is \(π10^2=100π\).

The answer is C.
Answer: C
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Intern
avatar
B
Joined: 15 Jun 2018
Posts: 4
Location: India
GMAT 1: 700 Q47 V38
CAT Tests
Re: If DB=2, AC=12, and X is the center of the circle shown as the above f  [#permalink]

Show Tags

New post 20 Jul 2018, 21:01
1
The solution assumes that line XB is perpendicular to line AC.

Can we assume that 2 lines are perpendicular without any information provided by the question?
GMAT Club Bot
Re: If DB=2, AC=12, and X is the center of the circle shown as the above f &nbs [#permalink] 20 Jul 2018, 21:01
Display posts from previous: Sort by

If DB=2, AC=12, and X is the center of the circle shown as the above f

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.