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

 It is currently 10 Dec 2019, 07:23 ### 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.  # In the Figure above, O is the center of a semicircle, and p

Author Message
TAGS:

### Hide Tags

Intern  Joined: 26 Dec 2011
Posts: 6
Schools: Yale '17 (A)
In the Figure above, O is the center of a semicircle, and p  [#permalink]

### Show Tags

4 00:00

Difficulty:   55% (hard)

Question Stats: 66% (02:32) correct 34% (02:27) wrong based on 110 sessions

### HideShow timer Statistics

Attachment: SemiCircle.jpg [ 12.87 KiB | Viewed 2421 times ]
In the Figure above, O is the center of a semicircle, and points A,B, C, D, and E lie on the semicircle. If the degree measure of angle AOC is 85, what is the degree measure of angle AOB?

(1) The degree measure of angle BOD is 100 degrees.

(2) The degree measure of angle COE is 95 degrees.

Source: Jeff Sackmann Geometry Challenge #97

OA is E, I think it is A. Attached is my reasoning.

Find angle AOB, say x
Given angle AOC is 85 degrees, then angle COD is 95 degrees ( 85+95 = 180)
Given that angle BOD is 100 degrees
Thus
<BOD = (<AOC - <AOB ) + ( <EOC - EOD )
100 = (85-x) + (95-y)
80 = x +y

Since this is a semi circle the two 'pies'; angle AOC and angle EOC are similar, thus
<AOC is to <AOB as <EOC is to <EOD
(85/x) = (95/y)

X = 17/19Y
Y = 19/17X
80 = x + y

Solve for X (<AOB)
(I am unsure of this final step involving similarity... Is this permitted/justified?)

Originally posted by NateTheGreat11 on 05 Sep 2013, 09:49.
Last edited by Bunuel on 05 Sep 2013, 10:00, edited 2 times in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 59632
Re: In the Figure above, O is the center of a semicircle, and p  [#permalink]

### Show Tags

1
NateTheGreat11 wrote: In the Figure above, O is the center of a semicircle, and points A,B, C, D, and E lie on the semicircle. If the degree measure of angle AOC is 85, what is the degree measure of angle AOB?

(1) The degree measure of angle BOD is 100 degrees.

(2) The degree measure of angle COE is 95 degrees.

Source: Jeff Sackmann Geometry Challenge #97

OA is E, I think it is A. Attached is my reasoning.

Find angle AOB, say x
Given angle AOC is 85 degrees, then angle COD is 95 degrees ( 85+95 = 180)
Given that angle BOD is 100 degrees
Thus
<BOD = (<AOC - <AOB ) + ( <EOC - EOD )
100 = (85-x) + (95-y)
80 = x +y

Since this is a semi circle the two 'pies'; angle AOC and angle EOC are similar, thus
<AOC is to <AOB as <EOC is to <EOD
(85/x) = (95/y)

X = 17/19Y
Y = 19/17X

80 = x + y

Solve for X (<AOB)
(I am unsure of this final step involving similarity... Is this permitted/justified?)

The red part is not correct. Check the diagram below:
Attachment: Angles.png [ 55.01 KiB | Viewed 2300 times ]
_________________
Senior Manager  S
Joined: 08 Jun 2015
Posts: 418
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38 GPA: 3.33
In the Figure above, O is the center of a semicircle, and p  [#permalink]

### Show Tags

E it is ..Neither of the two statements helps. Neither alone nor together ...
_________________
" The few , the fearless "
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8247
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: In the Figure above, O is the center of a semicircle, and p  [#permalink]

### Show Tags

If we consider degree AOB=x, degree BOC=y, degree COD=z and degree DOE=w, there are 4 variables (x,y,z and w) and 2 equations (x+y+z+w=180 and x+y=85) in the original condition. In order to match the number of equations and the number of variables, there are 2 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer.
Using the condition 1) and the condition 2) at the same time, we get y+z=100 and z+w=95. However, z+w=95 already appears in x+y=85. Hence, in overall, we lack 1 equation, which means the correct answer is E.

l For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________
Intern  B
Joined: 08 Jul 2018
Posts: 39
Re: In the Figure above, O is the center of a semicircle, and p  [#permalink]

### Show Tags

E You cannot determine the exact value.
Also i do not think that you can use similarity with the sectors of a circle, you will have to make some audacious assumptions to do so.
_________________

“Pain + Reflection = Progress”
― Ray Dalio
Non-Human User Joined: 09 Sep 2013
Posts: 13740
Re: In the Figure above, O is the center of a semicircle, and p  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: In the Figure above, O is the center of a semicircle, and p   [#permalink] 11 Aug 2019, 18:55
Display posts from previous: Sort by

# In the Figure above, O is the center of a semicircle, and p  