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

It is currently 18 Jun 2018, 13:51

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M09-37

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

Hide Tags

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46129
M09-37 [#permalink]

Show Tags

New post 16 Sep 2014, 00:41
3
4
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (00:59) correct 23% (02:04) wrong based on 121 sessions

HideShow timer Statistics

If in the picture below, the arc is a quarter of a circle and \(OABC\) is a rectangle, what is \(AC\)?

Image


A. \(5\sqrt{2}\)
B. \(7\sqrt{2}\)
C. 10
D. 12
E. \(9\sqrt{2}\)

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46129
Re M09-37 [#permalink]

Show Tags

New post 16 Sep 2014, 00:41
1
1
Official Solution:


If in the picture below, the arc is a quarter of a circle and \(OABC\) is a rectangle, what is \(AC\)?

Image


A. \(5\sqrt{2}\)
B. \(7\sqrt{2}\)
C. 10
D. 12
E. \(9\sqrt{2}\)

\(AC = OB\) is the radius of the circle, \(5 + 5 = 10\)

Answer: C
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 19 Sep 2014
Posts: 25
GPA: 3.96
GMAT ToolKit User Reviews Badge
Re: M09-37 [#permalink]

Show Tags

New post 27 Aug 2015, 08:23
Hi,
Could not understand that if AC=OB then why is 5 being added to 5 to get 10.The answer should be 5 only.Please explain where I am going wrong.
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46129
Re: M09-37 [#permalink]

Show Tags

New post 27 Aug 2015, 12:24
2
schak2rhyme wrote:
Hi,
Could not understand that if AC=OB then why is 5 being added to 5 to get 10.The answer should be 5 only.Please explain where I am going wrong.


AC is diagonal of the rectangle. The two diagonals of a rectangle are equal, thus AC = OB. But OB is also radius of the circle and radius of the circle according to the figure is 5 + 5 = 10.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Retired Moderator
avatar
B
Joined: 23 Sep 2015
Posts: 387
Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)
Premium Member Reviews Badge
Re: M09-37 [#permalink]

Show Tags

New post 25 Nov 2015, 07:16
I answerd the question by saying that it was a 30;60;90 triangle. Would this thinking be incorrect for this figure?
_________________

New Application Tracker : update your school profiles instantly!

Intern
Intern
User avatar
Joined: 27 Jul 2015
Posts: 6
Re: M09-37 [#permalink]

Show Tags

New post 15 Feb 2016, 06:34
Icecream87 wrote:
I answerd the question by saying that it was a 30;60;90 triangle. Would this thinking be incorrect for this figure?



Hi Icecream,

I did exactly the same!
In my opinion it is also a valid / possible way of solution.

@Bunuel, can you please advise?

Thanks!!
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46129
Re: M09-37 [#permalink]

Show Tags

New post 15 Feb 2016, 06:44
AnikaJu wrote:
Icecream87 wrote:
I answerd the question by saying that it was a 30;60;90 triangle. Would this thinking be incorrect for this figure?



Hi Icecream,

I did exactly the same!
In my opinion it is also a valid / possible way of solution.

@Bunuel, can you please advise?

Thanks!!


On what ground do you assume that the triangle is 30-60-90 triangle?
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
User avatar
Joined: 27 Jul 2015
Posts: 6
Re: M09-37 [#permalink]

Show Tags

New post 15 Feb 2016, 07:20
Bunuel wrote:
AnikaJu wrote:
Icecream87 wrote:
I answerd the question by saying that it was a 30;60;90 triangle. Would this thinking be incorrect for this figure?



Hi Icecream,

I did exactly the same!
In my opinion it is also a valid / possible way of solution.

@Bunuel, can you please advise?

Thanks!!


On what ground do you assume that the triangle is 30-60-90 triangle?




I know that the angle at point O is 90 degrees and the opposite of the angle of 90 degreed is 2x. x = 5.
However I must admit that I just assumed that the other two angles are 30 and 60, I cannot provide you a proof... mhmmmm :shock:

Thanks for your fast reply!
Intern
Intern
avatar
Joined: 22 Apr 2015
Posts: 12
GMAT 1: 760 Q50 V44
Re: M09-37 [#permalink]

Show Tags

New post 15 Apr 2016, 07:27
AnikaJu wrote:
Bunuel wrote:
AnikaJu wrote:

Hi Icecream,

I did exactly the same!
In my opinion it is also a valid / possible way of solution.

@Bunuel, can you please advise?

Thanks!!


On what ground do you assume that the triangle is 30-60-90 triangle?




I know that the angle at point O is 90 degrees and the opposite of the angle of 90 degreed is 2x. x = 5.
However I must admit that I just assumed that the other two angles are 30 and 60, I cannot provide you a proof... mhmmmm :shock:

Thanks for your fast reply!


So I did the same way, and while it's not the best way to solve, there's actually a way to prove that the triangle is a 30-60-90 triangle:

Since the object is a rectangle, angle OCA = angle COB. Because the rectangle is inscribed in the circle, we can also say that sin(angle COB) = 5/10 = .5. sin(30) = .5 so we know angle COB = OCA = 30 degrees.

Like I said, this was not at all the best way to answer this question, and I was getting way too analytical about it, but there you go.
Director
Director
User avatar
S
Joined: 24 Nov 2015
Posts: 562
Location: United States (LA)
Reviews Badge
Re: M09-37 [#permalink]

Show Tags

New post 18 Apr 2016, 15:11
diagonals of rectangle are equal in length.
from the figure the radius of circle is 10 units
OB = 10 units
therefore AC = 10 units
correct answer option C
Intern
Intern
avatar
Joined: 17 Aug 2016
Posts: 9
Re: M09-37 [#permalink]

Show Tags

New post 23 Oct 2016, 07:51
Pretty easy question, but for me it was not obvious that the two fives in the figure are measures of total length. I would have expected two points on the x-axis in order to dertermine the radius.
Intern
Intern
avatar
B
Joined: 23 Jun 2017
Posts: 1
Re M09-37 [#permalink]

Show Tags

New post 04 Sep 2017, 14:45
I think this is a poor-quality question and I don't agree with the explanation. This question's drawing is messed up. If you look at the chart it is very clear that what is explained later in the explanation as the "radius" (5+5), the 5 to the right of the 5 on the rectangle is on a line that goes through the edge of the Arc. The image makes it look like line AB is bisecting some line that starts at point O and goes through point A and through the edge of the Arc.

I would think on the gmat this wouldn't be the case, so I won't get up in arms about it. My original interpretation of the problem was "the radius (which will be equal to diagonal AC" will be less than 10 as (5+5) is represented in the image as a length greater than the radius.
Re M09-37   [#permalink] 04 Sep 2017, 14:45
Display posts from previous: Sort by

M09-37

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

Moderators: chetan2u, Bunuel



GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.