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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

Re: In the figure above, point O is the center of the circle and [#permalink]

Show Tags

29 Dec 2014, 21:09

How are we getting different variables x and y when the sides are equal. Can you explain Krishna. Cause three sides are equal shouldn't their angles be noted with the same variable?

Re: In the figure above, point O is the center of the circle and [#permalink]

Show Tags

29 Dec 2014, 21:14

I must have overlooked something because I get:

x+x+(180-2y)+y= 180 2x-y=0 2x-2x= 0[/quote]

Ignore the highlighted step. after 2x - y = 0, when you take y to the other side, you get 2x = y

Without doing this step, how did you substitute 2x for y in the highlighted step?[/quote] I see what I did. Below was my thought process:

x+x+(180-2y)+y= 180 2x-y=0 I then looked at the graph and applied the sum of two interior angles is equal to the opposite exterior which you labeled y. Once I got 2x= y I then went back to x+x+(180-2y)+y= 180 and thought I would end up with 5x= 180 but instead kept getting 2x-2x= 0

How are we getting different variables x and y when the sides are equal. Can you explain Krishna. Cause three sides are equal shouldn't their angles be noted with the same variable?

Note the sides that are equal OC = AC = AB

OC and AC are sides if a triangle and the angles opposite to them are marked as x each (i.e. they are equal)

AC and AB are equal sides of another triangle and angles opposite to them are marked as y each. Note that you cannot mark them as x too because they are equal angles in a different triangle. Their measure could be different from x. I have explained this in detail in a post given below. Giving the explanation here:

"When two sides of a triangle are equal, the two opposite angles are equal. But can you say what the two angles are? No. Say a triangle has two sides of length 5 cm each. Do we know the measure of equal angles? No. They could be 40-40 or 50-50 or 80-80 etc. So if you have two different triangles with 2 sides of length 5 cm each, the equal angle could have different measures - in one triangle the equal angles could be 50-50, in the other triangle, the equal angles could be 70-70.

In triangle OAC, since OC = AC, you have two equal angles as x each. The third angle here is 180 - 2x.

In triangle ACB, since AC = AB, angle ACB = angle ABC but what makes you say that they must be x each too? This is a different triangle. Even if the sides have the same length as the sides of triangle OAC, there is no reason to believe that the equal angles need to be x each. So you call the angles y. The third angle here is 180 - 2y."
_________________

x+x+(180-2y)+y= 180 2x-y=0 I then looked at the graph and applied the sum of two interior angles is equal to the opposite exterior which you labeled y. Once I got 2x= y I then went back to x+x+(180-2y)+y= 180 and thought I would end up with 5x= 180 but instead kept getting 2x-2x= 0

From this equation: x+x+(180-2y)+y= 180, you derive that 2x = y. If you try to substitute 2x = y in this equation itself, you will just get 2x - 2x = 0 which implies 0 = 0. This equation has 2 variables and you need two distinct equations to get the value of the two variables. If both equations are just 2x = y, you cannot get the value of x. You need another equation to get the value of x.
_________________

In the figure above, point O is the center of the circle and [#permalink]

Show Tags

25 Jul 2015, 19:40

1

This post received KUDOS

DropBear wrote:

Geometry: What is the angle of x?

Attachment:

The attachment Capture.PNG is no longer available

In the figure above, point O is the center of the circle and OC = AC = AB. What is the value of x?

A. 40 B. 36 C. 34 D. 32 E. 30

I had to guess this one recently and even after reading the official answer and explanation there are still some inferences that I just don't understand. I am really looking forward to seeing a few different ways of solving. Personally this is one of the hardest questions I have faced... Maybe you will find it easy

The reason for the poll is I would like to see how difficult everyone finds this question. As I said, this one really beat me!

Would be great to receive my first Kudos if you find this useful too

Straightforward question if you realize the additional constraint would come from the fact that in Triangle AOB, OA = OB = radius of the circle.

Now in triangle, ACO , \(\angle{COA} = \angle{OAC} = x\) (as OC = AC) and \(\angle{ACB} = 2x\) (external angle of a triangle)

Additionally, \(\angle{ACB}= \angle{ABC}\) = 2x (as AC = AB)

FInally, in triangle AOB, OA = OB = radius of the circle ---> \(\angle{OBA}=\angle{OAB}\) = 2x ---> \(\angle{CAB} =x\)

Thus , in triangle ACB,

\(\angle{ACB} + \angle{CBA} + \angle{BAC}\) =2x+2x+x = 180 ---> x = 36. B is the correct answer.

Please search for a question before posting.

Merged the posts.

Attachments

2015-07-25_22-46-01.jpg [ 6.8 KiB | Viewed 6105 times ]

Re: In the figure above, point O is the center of the circle and [#permalink]

Show Tags

03 Oct 2015, 11:17

Something it's not quite right here.

I'm also stuck with the last calculation.

STEP 1 180-2x + y = 180 2x = y OK I KNOW HOW TO FIND THIS

STEP 2 Then I convert Y to become 2X <AOB = x <ABO = 2x <BAO = x + (180-4x)-----Why I add x to 180-4x because that's how I think we get a straight line of 180 degree

therefore: x + 2x + x + (180-4x) = 180 then I get 180 = 180

STEP 1 180-2x + y = 180 2x = y OK I KNOW HOW TO FIND THIS

STEP 2 Then I convert Y to become 2X <AOB = x <ABO = 2x <BAO = x + (180-4x)-----Why I add x to 180-4x because that's how I think we get a straight line of 180 degree

therefore: x + 2x + x + (180-4x) = 180 then I get 180 = 180

PLEASE HELP ME. TOTALLY STUCK

After step 2, <BAO = <ABO x + 180 - 4x = 2x x = 36

The reason your third step doesn't work is because you used the property of total sum of triangle = 180 to get the relations. Now you are putting the relations back in sum of triangles is 180. You cannot get a value for x in this case. You need to put the relations in another property to arrive at a new conclusion (value of x).
_________________

Re: In the figure above, point O is the center of the circle and [#permalink]

Show Tags

09 Feb 2016, 01:09

Here, since OC=CA, angle OAC=x. Hence angle ACB=2x and ABC=2x If we extend BO to Q, then we get an inscribed angle AQB which is half the central angle x. and the angle QAB=90 so, x/2+2x+90=180 5x/2=90 x=36

Re: In the figure above, point O is the center of the circle and [#permalink]

Show Tags

23 Mar 2017, 07:42

I loved this question!

take a look at the triangle properties: if 2 sides are equal-then angles too so as oc=ac means that AOC=OAC x or AOB=180-2y as AC=AB -> ABC=ACB->CAB is x

this means that angles OAB is made up of x + x=y so x=180-2(2x)->5x=180, x=36

Re: In the figure above, point O is the center of the circle and [#permalink]

Show Tags

18 May 2017, 03:10

VeritasPrepKarishma wrote:

tonebeeze wrote:

In the figure attached, point O is the center of the circle and OC = AC = AB. What is the value of x (in degrees)?

a. 40 b. 36 c. 34 d. 32 e. 30

A small diagram helps:

Attachment:

Ques1.jpg

In the figure, you see (180 - 2x) + y = 180 (straight angle) so 2x = y

Also, the moment you see the circle and its two radii, mark them equal and the corresponding angles equal. (the red angle = blue angle) x + 180 - 2y = y 5x = 180 (from above, y = 2x) x = 36

good explanation but I am not understand (the red angle=blue angle )?

In the figure attached, point O is the center of the circle and OC = AC = AB. What is the value of x (in degrees)?

a. 40 b. 36 c. 34 d. 32 e. 30

A small diagram helps:

Attachment:

Ques1.jpg

In the figure, you see (180 - 2x) + y = 180 (straight angle) so 2x = y

Also, the moment you see the circle and its two radii, mark them equal and the corresponding angles equal. (the red angle = blue angle) x + 180 - 2y = y 5x = 180 (from above, y = 2x) x = 36

good explanation but I am not understand (the red angle=blue angle )?

OA and OB are radii of the same circle so they will be equal. So in triangle OAB, angle OAB = OBA ie. red angle = blue angle (in my diagram)
_________________

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

We know that OB and OA are radii of the circle, so their lengths are equal. And since OC = AC, we can denote their respective angles with x. For the supplementary angle of AC, we can use y and determine that 180-2x + y = 180 or 2x = y.

We also know that angle OAB = y, so x + 180 - 2y = y and thus x + 180 - 4x = 2x

Re: In the figure above, point O is the center of the circle and [#permalink]

Show Tags

30 Jul 2017, 09:10

Very tough question. A key is recognizing that since OB is a radius and OA is a radius therefore angle OAB = angle OBA. The rest is also very tricky. Attached is a diagram.

Attachments

hard gmat problem.png [ 313.1 KiB | Viewed 997 times ]