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

It is currently 23 Oct 2018, 05:05

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

M24-22

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
M24-22  [#permalink]

Show Tags

New post 16 Sep 2014, 01:21
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (01:11) correct 36% (01:12) wrong based on 133 sessions

HideShow timer Statistics

In triangle ABC, point O lies on side AC and segment BO is perpendicular to AC. If \(\angle BAO = \angle BCA = 45\) degrees and \(BC = 1\), what is the area of triangle ABO?

A. \(\frac{1}{4}\)
B. \(\frac{1}{2}\)
C. 1
D. \(\sqrt{2}\)
E. 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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
Re M24-22  [#permalink]

Show Tags

New post 16 Sep 2014, 01:21
Official Solution:

In triangle ABC, point O lies on side AC and segment BO is perpendicular to AC. If \(\angle BAO = \angle BCA = 45\) degrees and \(BC = 1\), what is the area of triangle ABO?

A. \(\frac{1}{4}\)
B. \(\frac{1}{2}\)
C. 1
D. \(\sqrt{2}\)
E. 2

Triangle ABC is right-angled and isosceles. Its area \(= 1*\frac{1}{2} = \frac{1}{2}\). The area of triangle ABO = half the area of triangle ABC \(= \frac{1}{4}\).

Answer: A
_________________

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: 11 Nov 2014
Posts: 34
Concentration: Technology, Strategy
GMAT 1: 660 Q48 V31
GMAT 2: 720 Q50 V37
GPA: 3.6
WE: Consulting (Consulting)
GMAT ToolKit User
Re: M24-22  [#permalink]

Show Tags

New post 18 Jun 2015, 10:30
Bunuel

Can you explain if the formula Side of A/Side of B = (Area of A/Area of B)^2 would be applicable to this case? IF not, why? And if yes, how?
PS: Your solution is much simpler, but just in case...
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
Re: M24-22  [#permalink]

Show Tags

New post 19 Jun 2015, 01:03
michaelyb wrote:
Bunuel

Can you explain if the formula Side of A/Side of B = (Area of A/Area of B)^2 would be applicable to this case? IF not, why? And if yes, how?
PS: Your solution is much simpler, but just in case...


It should be \(\frac{AREA}{area}=\frac{SIDE^2}{side^2}\).

Well, yes you can do this way too by realizing that both triangles BOC and ABC are 45-45-90 and thus similar. Then you can find the area of ABC (1/2), AC (\(\sqrt{2}\)) and then AC/BC = (area of ABC)^2/((area of AOC)^2):

\((\frac{\sqrt{2}}{1})^2 = \frac{1/2}{x}\) --> x = 1/4.

But, this is not a good way to solve.
_________________

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: 11 Nov 2014
Posts: 34
Concentration: Technology, Strategy
GMAT 1: 660 Q48 V31
GMAT 2: 720 Q50 V37
GPA: 3.6
WE: Consulting (Consulting)
GMAT ToolKit User
Re: M24-22  [#permalink]

Show Tags

New post 19 Jun 2015, 04:48
Thanks, Bunuel!
Very helpful, as usual.
Manager
Manager
avatar
B
Joined: 14 Aug 2012
Posts: 59
GMAT 1: 620 Q43 V33
Premium Member CAT Tests
Re: M24-22  [#permalink]

Show Tags

New post 09 May 2018, 02:22
Does anyone have a picture explanation? I am not seeing the hint indicating that ABO triangle is 1/2 the area of ABC
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
M24-22  [#permalink]

Show Tags

New post 09 May 2018, 02:35
1
bpdulog wrote:
In triangle ABC, point O lies on side AC and segment BO is perpendicular to AC. If \(\angle BAO = \angle BCA = 45\) degrees and \(BC = 1\), what is the area of triangle ABO?


A. \(\frac{1}{4}\)
B. \(\frac{1}{2}\)
C. 1
D. \(\sqrt{2}\)
E. 2

Triangle ABC is right-angled and isosceles. Its area \(= 1*\frac{1}{2} = \frac{1}{2}\). The area of triangle ABO = half the area of triangle ABC \(= \frac{1}{4}\).

Answer: ADoes anyone have a picture explanation? I am not seeing the hint indicating that ABO triangle is 1/2 the area of ABC


Here it is:

Image

Hope it helps.


Attachment:
Triangle.png

>> !!!

You do not have the required permissions to view the files attached to this post.


_________________

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
B
Joined: 22 Apr 2017
Posts: 1
CAT Tests
M24-22  [#permalink]

Show Tags

New post 31 Jul 2018, 12:44
In this case, wouldn't the value of AC be sqrt 2.

If so, it would then lead AO = (sqrt 2)/2 (half of the base of isosceles triangle)
Then BO = 1/2
Area of AOB = 1/2*1/2*(sqrt 2)/2

If we follow this approach, where we are still considering triangle AOB as half, why is the solution different from 1/4?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
M24-22  [#permalink]

Show Tags

New post 31 Jul 2018, 20:42
Vineela.mk wrote:
In this case, wouldn't the value of AC be sqrt 2.

If so, it would then lead AO = (sqrt 2)/2 (half of the base of isosceles triangle)
Then BO = 1/2
Area of AOB = 1/2*1/2*(sqrt 2)/2

If we follow this approach, where we are still considering triangle AOB as half, why is the solution different from 1/4?


Image

Yes, \(AC = \sqrt{2}\) and \(AO=\frac{\sqrt{2}}{2}\) but BO is not 1/2. \(BO = AO = \frac{\sqrt{2}}{2}\) because BAO is also isosceles. If you proceed from here you'll get the same answer as in the solution.
_________________

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

GMAT Club Bot
M24-22 &nbs [#permalink] 31 Jul 2018, 20:42
Display posts from previous: Sort by

M24-22

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

Moderators: chetan2u, Bunuel



Copyright

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®.