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

 It is currently 19 Mar 2019, 18:11 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # In the figure above, point O is the center of the circle and OC = AC =

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

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 53709
In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

19
157 00:00

Difficulty:   95% (hard)

Question Stats: 60% (02:55) correct 40% (02:54) wrong based on 2215 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition 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
(0) 32
(E) 30

Problem Solving
Question: 162
Category: Arithmetic Statistics
Page: 83
Difficulty: 600

Attachment: Untitled.png [ 13.16 KiB | Viewed 329214 times ]

_________________

Originally posted by Bunuel on 16 Jan 2011, 16:56.
Last edited by Bunuel on 04 Feb 2019, 04:59, edited 5 times in total.
Renamed the topic and edited the question.
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 8988
Location: Pune, India
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

71
33
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 [ 9.23 KiB | Viewed 259351 times ]

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
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Director  Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 992
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

24
1
7
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

It goes like this -

In triangle OAB , Angle O + Angle A + Angle B = 180 -------1
OA = OB (Radius) => Angle A = Angle B

In triangle ACB, Angle C = Angle O + Angle OAC (Sum of interior opposite angles)
=> Angle ACB = 2x;
Also, AC = AB => Angle ACB = Angle ABC = 2x each

Thus Angle A = Angle B = 2x each.

So, substituting in 1

5x = 180 => x = 36 deg.

This will help.
##### General Discussion
Director  B
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 503
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

1
angle oac=x
angle acb=2x=angle b=2x=a (as oa and ob are radii)
so in triangle oab x+2x+3x=180
x=36
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Senior Manager  Joined: 13 May 2013
Posts: 421
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

4
2
In the figure attached, point O is the center of the circle and OC = AC = AB. What is the value of x (in degrees)?

OC = AC = AB tells us that triangle OAC and BAC are isosceles. Also, as with any triangle on a straight line with an exterior angle, the exterior angle (or in this case, angle ACB) can be found by subtracting the interior angle from 180.

We know that in triangle OAC (because it is an isosceles triangle) that angle o and angle a are equal to one another. Therefore, angle c = 180 - x - x --> angle c = 180-2x. Angle C (of the smaller isosceles triangle) also happens to share the same angle measurement as angle B. Furthermore, because OA and OB are radii, we know that they equal one another and that angle A = angle B.

We know that angle c in the smaller isosceles triangle = 180 - the measure of the obtuse angle C. As shown above the obtuse angle C = (180-2x) So, the small angle C = 180 - (180-2x) --> angle C = 2x. So, angle C = B = 2x. If angle A = B then A = 2x and becaause the obtuse triangle has two x measurements, we know that the measure of A in the small isosceles triangle = x. Therefore, in the small isosceles triangle we have 2x+2x+x = 180. 5x = 180. x = 36.

b. 36
Manager  Joined: 15 Aug 2013
Posts: 243
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

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

Hi Karishma,

Thanks for the detailed explanation but I still have a nagging issue. I was having a hard time setting this up with the variables. For example, <OAC, you have it broken up as 180-2y and x, which i see why you did. When I started working on this problem, I labeled <ACB and <ABC as "x" because of the congruent lines and I labeled OAC and COA as "x" too because all of those lines were same according to the question stem. Doing so, conflicted with the fact that <OAB and <ABO are equal and that's when my whole setup went kaboom Why is that wrong?

I guess I'm not following why you gave some variables "x" vs. some "y"?

Thanks!
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 8988
Location: Pune, India
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

4
russ9 wrote:
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

Hi Karishma,

Thanks for the detailed explanation but I still have a nagging issue. I was having a hard time setting this up with the variables. For example, <OAC, you have it broken up as 180-2y and x, which i see why you did. When I started working on this problem, I labeled <ACB and <ABC as "x" because of the congruent lines and I labeled OAC and COA as "x" too because all of those lines were same according to the question stem. Doing so, conflicted with the fact that <OAB and <ABO are equal and that's when my whole setup went kaboom Why is that wrong?

I guess I'm not following why you gave some variables "x" vs. some "y"?

Thanks!

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.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1817
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

47
8
Answer = B = 36

Please refer diagram below:
Attachments as.jpg [ 39.56 KiB | Viewed 250088 times ]

_________________

Kindly press "+1 Kudos" to appreciate Manager  Joined: 15 Aug 2013
Posts: 243
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

VeritasPrepKarishma wrote:
russ9 wrote:

Hi Karishma,

Thanks for the detailed explanation but I still have a nagging issue. I was having a hard time setting this up with the variables. For example, <OAC, you have it broken up as 180-2y and x, which i see why you did. When I started working on this problem, I labeled <ACB and <ABC as "x" because of the congruent lines and I labeled OAC and COA as "x" too because all of those lines were same according to the question stem. Doing so, conflicted with the fact that <OAB and <ABO are equal and that's when my whole setup went kaboom Why is that wrong?

I guess I'm not following why you gave some variables "x" vs. some "y"?

Thanks!

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.

Hi Karishma,

This is news to me -- you can't assume that because length AC is shared, that implies that the corresponding angle in Triangle ACO will equal the corresponding angle in ACB?

Hmm -- learn something new everyday! Thanks!
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 8988
Location: Pune, India
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

russ9 wrote:

Hi Karishma,

This is news to me -- you can't assume that because length AC is shared, that implies that the corresponding angle in Triangle ACO will equal the corresponding angle in ACB?

Hmm -- learn something new everyday! Thanks!

Corresponding angles are equal only when you have parallel lines with a common transversal.
Make two triangles with a common side. Can you make the angles made on the common side such that the angles have very different measures? Sure!

Attachment: Ques3.jpg [ 6.81 KiB | Viewed 249647 times ]

Here one angle is 90 degrees and the other is acute.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Intern  Joined: 20 Dec 2014
Posts: 19
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

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

Karishma - why is it that you did not have x+ x + (180 - 2y)+ y = 180 to include the entire triangle? I solved this equation by adding an additional line to form a diameter and then constructed another angle(titled z) and approached the solution that way but I am attempting to understand this method that you used to solve this problem.
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 8988
Location: Pune, India
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

GMAT01 wrote:
Karishma - why is it that you did not have x+ x + (180 - 2y)+ y = 180 to include the entire triangle? I solved this equation by adding an additional line to form a diameter and then constructed another angle(titled z) and approached the solution that way but I am attempting to understand this method that you used to solve this problem.

You need to find the relation between x and y. You can do it in any way you like; you will get the same result.

Doing it your way:
x+ x + (180 - 2y)+ y = 180
2x = y
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Intern  Joined: 20 Dec 2014
Posts: 19
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

VeritasPrepKarishma wrote:
GMAT01 wrote:
Karishma - why is it that you did not have x+ x + (180 - 2y)+ y = 180 to include the entire triangle? I solved this equation by adding an additional line to form a diameter and then constructed another angle(titled z) and approached the solution that way but I am attempting to understand this method that you used to solve this problem.

You need to find the relation between x and y. You can do it in any way you like; you will get the same result.

Doing it your way:
x+ x + (180 - 2y)+ y = 180
2x = y

Thank you.

I must have overlooked something because I get:

x+x+(180-2y)+y= 180
2x-y=0
2x-2x= 0
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 8988
Location: Pune, India
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

GMAT01 wrote:
VeritasPrepKarishma wrote:
GMAT01 wrote:
Karishma - why is it that you did not have x+ x + (180 - 2y)+ y = 180 to include the entire triangle? I solved this equation by adding an additional line to form a diameter and then constructed another angle(titled z) and approached the solution that way but I am attempting to understand this method that you used to solve this problem.

You need to find the relation between x and y. You can do it in any way you like; you will get the same result.

Doing it your way:
x+ x + (180 - 2y)+ y = 180
2x = y

Thank you.

I must have overlooked something because I get:

x+x+(180-2y)+y= 180
2x-y=0
2x-2x= 0

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?
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager  B
Joined: 27 May 2014
Posts: 79
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

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?
Intern  Joined: 20 Dec 2014
Posts: 19
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

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
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 8988
Location: Pune, India
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

bankerboy30 wrote:
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."
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 8988
Location: Pune, India
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

1
GMAT01 wrote:
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

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.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager  Joined: 26 Feb 2015
Posts: 114
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

What step am I doing wrong here? I can't figure it out. I don't understand how to go to 5x = 180

I just get to 4x + 180 - 4x = 180 aka 4x - 4x = 0..

edit: that last "8" kinda looks like a 5, but its supposed to be an 8 e-GMAT Representative D
Joined: 04 Jan 2015
Posts: 2709
Re: In the figure above, point O is the center of the circle and OC = AC =  [#permalink]

### Show Tags

2
1
erikvm wrote:
What step am I doing wrong here? I can't figure it out. I don't understand how to go to 5x = 180

I just get to 4x + 180 - 4x = 180 aka 4x - 4x = 0..

edit: that last "8" kinda looks like a 5, but its supposed to be an 8 Hi erikvm, The angle which you have written as 180 - 2y = x because OA = OB (radii of the circle). So ∠OAB = ∠OBA.

∠(OAC + CAB) = y = 2x
x + ∠CAB = 2x which gives us ∠CAB = x.

Now summing up the angles in triangle OAB, we get x + 2x + 2x = 180 i.e. x = 36

Hope this helps Regards
Harsh
_________________  Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Session:- Key strategy to score 760

Success Stories
Q38 to Q50- Interview call form Wharton | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com Re: In the figure above, point O is the center of the circle and OC = AC =   [#permalink] 18 May 2015, 11:19

Go to page    1   2    Next  [ 34 posts ]

Display posts from previous: Sort by

# In the figure above, point O is the center of the circle and OC = AC =

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