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

It is currently 18 Jun 2018, 18:00
Search
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar
CLICK HERE TO HIDE/SHOW EVENTS

The area of rectangle ABCD is closest to which of the following?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
  Sort by Date Sort by Kudos  
Search for:
 
Print view
First unread post
Author Message
TAGS:

Hide Tags
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46129
Premium Member CAT Tests
Top Member of the Month
The area of rectangle ABCD is closest to which of the following? [#permalink]

Show Tags

New post 07 May 2015, 04:05
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (00:40) correct 31% (00:56) wrong based on 131 sessions

HideShow timer Statistics

Image
The area of rectangle ABCD is closest to which of the following?

(A) 100
(B) 130
(C) 170
(D) 200
(E) 230

Spoiler: ::
Attachment:
drawn-1.png
drawn-1.png [ 4.01 KiB | Viewed 1937 times ]


Kudos for a correct solution.
Spoiler: OA

_________________

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

1 KUDOS received
Intern
Intern
User avatar
Joined: 25 Nov 2014
Posts: 5
GMAT 1: 670 Q48 V34
The area of rectangle ABCD is closest to which of the following? [#permalink]

Show Tags

New post Updated on: 07 May 2015, 06:56
1
Let length be: L
tan 30 deg = 10/L

Since, tan 30 deg = 1/\(\sqrt{3}\)

1/\(\sqrt{3}\) = 10/L


L = 10*\(\sqrt{3}\)
(\(\sqrt{3}\) ~ 1.732)
Therefore, L = 17.32

Now, area is 10*L, ie. 10*17.32 = 173.2 ~ 170

Answer: C

Originally posted by ApurbaGMAT on 07 May 2015, 06:49.
Last edited by ApurbaGMAT on 07 May 2015, 06:56, edited 1 time in total.
1 KUDOS received
Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 177
Re: The area of rectangle ABCD is closest to which of the following? [#permalink]

Show Tags

New post 07 May 2015, 06:55
1
As we know that Arc ACD is 30 degrees and arc DAC is 90 degrees we can infer that the remaining arc in the upper right area has to be 60 degrees as a triangle has a maximum of 180 degrees.

This yields a 30-60-90 triangle with side relationship of x - x sqrt 3 - 2x. X in this case is 10, therefore we can derive the other sides and also the bottom side of the rectangle.

In my calculation this results in an area of approx. 170!
1 KUDOS received
Manager
Manager
User avatar
Joined: 03 Sep 2014
Posts: 74
Concentration: Marketing, Healthcare
Schools: Kellogg 1YR '17, Booth '16, McCombs '18, Tepper '18, INSEAD Jan '17, ISB '17, NUS '18, IIMA , IIMB, IIMC , IIM-L '15
Premium Member
Re: The area of rectangle ABCD is closest to which of the following? [#permalink]

Show Tags

New post 07 May 2015, 09:15
1
Bunuel wrote:
Image
The area of rectangle ABCD is closest to which of the following?

(A) 100
(B) 130
(C) 170
(D) 200
(E) 230

Spoiler: ::
Attachment:
drawn-1.png


Kudos for a correct solution.


Triangle ABC or ACD are 30-60-90 triangle, thus, AD= \(a\sqrt{3} = 10\sqrt{3} = 17 => Area = 10*17 = 170\)

Hence Answer is C
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46129
Premium Member CAT Tests
Top Member of the Month
The area of rectangle ABCD is closest to which of the following? [#permalink]

Show Tags

New post 11 May 2015, 04:01
Bunuel wrote:
Image
The area of rectangle ABCD is closest to which of the following?

(A) 100
(B) 130
(C) 170
(D) 200
(E) 230

Spoiler: ::
Attachment:
drawn-1.png


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

Suppose we don't know the math to answer this question. We are told it's a rectangle, so we know the angles must be right angles, and we know the area must be length (AD) times height (AB). We know the height is 10. We know AD is drawn to scale. It definitely is longer than AB, so the area is definitely larger than 10 x 10 (answer (A) is out). AD doesn't look as long as twice AB, so the area is definitely less than 10 x 20 (answers (D) & (E) are out). Notice, with pure spatial estimation, we eliminated three of the five answer choices, so it will be to our advantage to guess randomly from the remaining two if we can't decide between them. Estimating from size can be a huge help if you don't remember the way to solve the problem.

BTW, the real math solution to that question: from the properties of the 30-60-90 triangle (ACD), we know that \(AD = 10*\sqrt{3}\), and since \(\sqrt{3}\) is approximately 1.7, AD is approximately 17, and the area is approximately 170.

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

Manager
Manager
avatar
B
Joined: 23 Oct 2017
Posts: 64
Re: The area of rectangle ABCD is closest to which of the following? [#permalink]

Show Tags

New post 10 Jan 2018, 19:24
Bunuel wrote:
Image
The area of rectangle ABCD is closest to which of the following?

(A) 100
(B) 130
(C) 170
(D) 200
(E) 230

Spoiler: ::
Attachment:
drawn-1.png


Kudos for a correct solution.

--------------------
Let the length of the diagonal be h.
h*cos 60 = 10 (=b)
h*(1/2)=10
h=20

l*l + b*b =20*20
since b =10
=> l = 10 * sqrt(3)
Area =l*b = 10 * sqrt(3) * 10
=100 * sqrt(3)
=100 * 1.732
=173.2 closest to 170
Re: The area of rectangle ABCD is closest to which of the following?   [#permalink] 10 Jan 2018, 19:24
Print view
First unread post
Display posts from previous: Sort by

The area of rectangle ABCD is closest to which of the following?

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

Moderators: chetan2u, Bunuel, niks18, mikemcgarry, VeritasPrepKarishma, generis

Search for:


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®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions