Sep 22 08:00 PM PDT  09:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE Sep 23 08:00 AM PDT  09:00 AM PDT Join a free 1hour webinar and learn how to create the ultimate study plan, and be accepted to the upcoming Round 2 deadlines. Save your spot today! Monday, September 23rd at 8 AM PST
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 457
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

If CD is the diameter of the circle, does x equal 30?
[#permalink]
Show Tags
05 Feb 2012, 17:08
Question Stats:
72% (01:08) correct 28% (01:16) wrong based on 326 sessions
HideShow timer Statistics
Attachment:
Triangle.jpg [ 13.63 KiB  Viewed 13962 times ]
If CD is the diameter of the circle, does x equal 30? (1) The length of CD is twice the length of BD. (2) y = 60 This is how I am trying to solve this, but there is bit of a guess work. So can someone please help?
Considering the figure CD is the diameter of the circle and its the hypotenuse of the triangle too i.e. Angle CBD= 90 degrees. (1). This is where I am guessing.
If that's the case then considering statement 1
Knowing that the side ratios of the 30:60:90 degree triangle are 1:\(\sqrt{3}\):2 the know that the x = 30 and y = 60 as the x is the angle opposite to the shortest leg. Therefore, sufficient.
Statement 2
x + y + B = 180 x+60+90 = 180 x = 30. Sufficient.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730




Math Expert
Joined: 02 Sep 2009
Posts: 58142

Re: Is angle x = 30 degrees?
[#permalink]
Show Tags
05 Feb 2012, 18:01
Attachment:
Triangle.jpg [ 13.63 KiB  Viewed 13918 times ]
If CD is the diameter of the circle, does x equal 30?A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle. So, angle CBD is a right angle. (1) The length of CD is twice the length of BD > ratio of a hypotenuse to a side is 2:1 > we have 30°, 60°, and 90° right triangle, where the sides are always in the ratio \(1:\sqrt{3}:2\). BD corresponds with 1, thus it's smallest side and opposite the smallest angle (30°). Sufficient. (2) y = 60. x=1809060=30. Sufficient. Answer: D.
_________________




Retired Moderator
Joined: 23 Jul 2010
Posts: 425
GPA: 3.4
WE: General Management (NonProfit and Government)

Re: Is angle x = 30 degrees?
[#permalink]
Show Tags
05 Feb 2012, 18:05
enigma123 wrote: If CD is the diameter of the circle, does x equal 30?
(1) The length of CD is twice the length of BD. (2) y = 60
This is how I am trying to solve this, but there is bit of a guess work. So can someone please help?
Considering the figure CD is the diameter of the circle and its the hypotenuse of the triangle too i.e. Angle CBD= 90 degrees. (1). This is where I am guessing.
Hi,You are right in your logic. In fact what you are guessing is actually true ,with respect to the figure If the hypotenuse of the triangle is also the diameter of the circle , then the angle opposite to it is a right angle . In other words 'the angle inscribed by the diameter of a circle is a right angle'.
_________________



Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 457
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

Re: If CD is the diameter of the circle, does x equal 30?
[#permalink]
Show Tags
05 Feb 2012, 18:10
Agree dentobizz and Bunuel  but no where in question says that its a diameter  so are we assuming or am I missing something?
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730



Retired Moderator
Joined: 23 Jul 2010
Posts: 425
GPA: 3.4
WE: General Management (NonProfit and Government)

Re: If CD is the diameter of the circle, does x equal 30?
[#permalink]
Show Tags
05 Feb 2012, 18:16
enigma123 wrote: If CD is the diameter of the circle, does x equal 30?
CD is the diameter of the circle as given in the question stem
_________________



Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 457
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

Re: If CD is the diameter of the circle, does x equal 30?
[#permalink]
Show Tags
05 Feb 2012, 18:16
My sincere apologies. I agree and thanks to both of you.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730



Intern
Joined: 30 Oct 2012
Posts: 18
Location: United States
Concentration: General Management, Entrepreneurship
WE: Science (Transportation)

Re: Triangle Inscribed
[#permalink]
Show Tags
10 Jan 2013, 12:29
D
If CD is a diameter then triangle BCD is a right angle triangle with angle B = 90.
For triangle BCD, angle B +x +y = 180
Therefore we know that x+y=90.
1) . CD = 2 x BD.
By Pythagorus Theorem, CD x CD = (BD x BD) + (BC x BC)
=> (BCxBC) = 4 (BDxBD)  (BDxBD) = 3 (BDxBD) => BC = \sqrt{3} BD
Tan x = BD / BC = BD/(\sqrt{3}BD) = 1/\sqrt{3}
=> x = 30
SUFFICIENT
2) y=60
& x+y=90
=> x= 9060 = 30
SUFFICIENT



Intern
Joined: 10 Jan 2014
Posts: 22

Re: Is angle x = 30 degrees?
[#permalink]
Show Tags
27 Feb 2014, 05:52
Bunuel wrote: Attachment: Triangle.jpg If CD is the diameter of the circle, does x equal 30?A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle. So, angle CBD is a right angle. (1) The length of CD is twice the length of BD > ratio of a hypotenuse to a side is 2:1 > we have 30°, 60°, and 90° right triangle, where the sides are always in the ratio \(1:\sqrt{3}:2\). BD corresponds with 1, thus it's smallest side and opposite the smallest angle (30°). Sufficient. (2) y = 60. x=1809060=30. Sufficient. Answer: D. I am having difficulties applying ratios in triangles. If CD=2BD then the their ratio is (CD/BD)= 2. Based on this, shouldn't the ratio of their corresponding angles (90° corresponds to side CD, and x° corresponds to BD) be the same? So, (90°/x°)=2 > x°=45° I know this is wrong, and I understand the explanation using the 306090 ratio but I don't understand why my ratio lead to the wrong solution. I hope someone can clarify this for me cheers, Max



Math Expert
Joined: 02 Sep 2009
Posts: 58142

Re: Is angle x = 30 degrees?
[#permalink]
Show Tags
27 Feb 2014, 06:21
damamikus wrote: Bunuel wrote: Attachment: Triangle.jpg If CD is the diameter of the circle, does x equal 30?A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle. So, angle CBD is a right angle. (1) The length of CD is twice the length of BD > ratio of a hypotenuse to a side is 2:1 > we have 30°, 60°, and 90° right triangle, where the sides are always in the ratio \(1:\sqrt{3}:2\). BD corresponds with 1, thus it's smallest side and opposite the smallest angle (30°). Sufficient. (2) y = 60. x=1809060=30. Sufficient. Answer: D. I am having difficulties applying ratios in triangles. If CD=2BD then the their ratio is (CD/BD)= 2. Based on this, shouldn't the ratio of their corresponding angles (90° corresponds to side CD, and x° corresponds to BD) be the same? So, (90°/x°)=2 > x°=45° I know this is wrong, and I understand the explanation using the 306090 ratio but I don't understand why my ratio lead to the wrong solution. I hope someone can clarify this for me cheers, Max In a triangle the ratios of the sides and the ratios of the angles not necessarily equal to each other.
_________________



Intern
Joined: 14 Aug 2016
Posts: 1

Re: If CD is the diameter of the circle, does x equal 30?
[#permalink]
Show Tags
16 Sep 2016, 06:00
Another, simple explanation why (1) is sufficient:
CB is an inscribed chord with a length equalling the radius of the circle. Every point on the circle has an equal distance (i.e. the radius) to the center. Drawing a triangle OCB (O being the center) reveals that OC=CB=OB and <OCB = 60 degrees. 1806090=30 for the angles of the big triangle. (1) is sufficient.



Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 364

Re: If CD is the diameter of the circle, does x equal 30?
[#permalink]
Show Tags
20 Sep 2016, 13:12
Definitely vote D.
Initial statement lets us know we are dealing with a right triangle
(1) SUFFICIENT  angle that is opposite 2x with be 2x the angle remaining  Thus we know we are dealing with a 306090 triangle
(2) SUFFICIENT  we know two angles and thus we can solve for the third



Senior Manager
Joined: 24 Nov 2016
Posts: 454
Location: United States

Re: If CD is the diameter of the circle, does x equal 30?
[#permalink]
Show Tags
21 Jun 2019, 14:48
Bunuel wrote: Attachment: Triangle.jpg If CD is the diameter of the circle, does x equal 30?A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle. So, angle CBD is a right angle. (1) The length of CD is twice the length of BD > ratio of a hypotenuse to a side is 2:1 > we have 30°, 60°, and 90° right triangle, where the sides are always in the ratio \(1:\sqrt{3}:2\). BD corresponds with 1, thus it's smallest side and opposite the smallest angle (30°). Sufficient. (2) y = 60. x=1809060=30. Sufficient. Answer: D. Hey Bunuel, the question doesn't say that the triangle BCD is inscribed in the circle  so Point B could be anywhere. What am I missing?



Manager
Joined: 04 Jun 2017
Posts: 110
Location: India
Concentration: Strategy, Operations
GPA: 3.82

Re: If CD is the diameter of the circle, does x equal 30?
[#permalink]
Show Tags
21 Jun 2019, 19:45
If CD is a diameter then triangle BCD is a right angle triangle with angle B = 90.
For triangle BCD, angle B +x +y = 180
Therefore we know that x+y=90.
1) . CD = 2 x BD.
By Pythagorus Theorem, Tan 1/root 3 = 30 degree => x = 30
SUFFICIENT
2) y=60
& x+y=90
=> x= 9060 = 30
SUFFICIENT
D is correct



Manager
Joined: 17 Jul 2017
Posts: 164

Re: If CD is the diameter of the circle, does x equal 30?
[#permalink]
Show Tags
02 Aug 2019, 07:07
Bunuel wrote: Attachment: Triangle.jpg If CD is the diameter of the circle, does x equal 30?A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle. So, angle CBD is a right angle. (1) The length of CD is twice the length of BD > ratio of a hypotenuse to a side is 2:1 > we have 30°, 60°, and 90° right triangle, where the sides are always in the ratio \(1:\sqrt{3}:2\). BD corresponds with 1, thus it's smallest side and opposite the smallest angle (30°). Sufficient. (2) y = 60. x=1809060=30. Sufficient. Answer: D. BunuelI understand that if trainagle has ratio 1:root3:2 it is 30 60 90 here we know hyp ther side is 2:1 and one angle is 90 so is this sufficent to conclude that if ratio of two sides is 2:1 and one angle is 90 it is 30 60 90 traingle ?




Re: If CD is the diameter of the circle, does x equal 30?
[#permalink]
02 Aug 2019, 07:07






