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

It is currently 26 Aug 2019, 03:03

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

If CD is the diameter of the circle, does x equal 30?

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

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 461
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
If CD is the diameter of the circle, does x equal 30?  [#permalink]

Show Tags

New post 05 Feb 2012, 17:08
1
12
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

72% (01:08) correct 28% (01:17) wrong based on 319 sessions

HideShow timer Statistics

Attachment:
Triangle.jpg
Triangle.jpg [ 13.63 KiB | Viewed 13682 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.

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57298
Re: Is angle x = 30 degrees?  [#permalink]

Show Tags

New post 05 Feb 2012, 18:01
1
6
Attachment:
Triangle.jpg
Triangle.jpg [ 13.63 KiB | Viewed 13639 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=180-90-60=30. Sufficient.

Answer: D.
_________________
General Discussion
Retired Moderator
avatar
B
Joined: 23 Jul 2010
Posts: 427
GPA: 3.4
WE: General Management (Non-Profit and Government)
GMAT ToolKit User
Re: Is angle x = 30 degrees?  [#permalink]

Show Tags

New post 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
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 461
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: If CD is the diameter of the circle, does x equal 30?  [#permalink]

Show Tags

New post 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
avatar
B
Joined: 23 Jul 2010
Posts: 427
GPA: 3.4
WE: General Management (Non-Profit and Government)
GMAT ToolKit User
Re: If CD is the diameter of the circle, does x equal 30?  [#permalink]

Show Tags

New post 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
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 461
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: If CD is the diameter of the circle, does x equal 30?  [#permalink]

Show Tags

New post 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
Intern
avatar
Joined: 30 Oct 2012
Posts: 18
Location: United States
Concentration: General Management, Entrepreneurship
GMAT 1: 750 Q50 V40
WE: Science (Transportation)
Reviews Badge
Re: Triangle Inscribed  [#permalink]

Show Tags

New post 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= 90-60 = 30

SUFFICIENT
Intern
Intern
avatar
Joined: 10 Jan 2014
Posts: 22
Re: Is angle x = 30 degrees?  [#permalink]

Show Tags

New post 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=180-90-60=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 30-60-90 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
User avatar
V
Joined: 02 Sep 2009
Posts: 57298
Re: Is angle x = 30 degrees?  [#permalink]

Show Tags

New post 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=180-90-60=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 30-60-90 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
Intern
avatar
Joined: 14 Aug 2016
Posts: 1
Re: If CD is the diameter of the circle, does x equal 30?  [#permalink]

Show Tags

New post 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. 180-60-90=30 for the angles of the big triangle. (1) is sufficient.
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 367
Re: If CD is the diameter of the circle, does x equal 30?  [#permalink]

Show Tags

New post 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 30-60-90 triangle

(2) SUFFICIENT - we know two angles and thus we can solve for the third
Senior Manager
Senior Manager
avatar
G
Joined: 24 Nov 2016
Posts: 341
Location: United States
CAT Tests
Re: If CD is the diameter of the circle, does x equal 30?  [#permalink]

Show Tags

New post 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=180-90-60=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
Manager
User avatar
B
Joined: 04 Jun 2017
Posts: 106
Location: India
Concentration: Strategy, Operations
GMAT 1: 500 Q39 V20
GPA: 3.82
CAT Tests
Re: If CD is the diameter of the circle, does x equal 30?  [#permalink]

Show Tags

New post 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= 90-60 = 30

SUFFICIENT

D is correct
Manager
Manager
avatar
S
Joined: 17 Jul 2017
Posts: 119
Re: If CD is the diameter of the circle, does x equal 30?  [#permalink]

Show Tags

New post 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=180-90-60=30. Sufficient.

Answer: D.

Bunuel
I understand that if trainagle has ratio 1:root3:2 it is 30 60 90
here we know hyp :other 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 ?
GMAT Club Bot
Re: If CD is the diameter of the circle, does x equal 30?   [#permalink] 02 Aug 2019, 07:07
Display posts from previous: Sort by

If CD is the diameter of the circle, does x equal 30?

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





cron

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