Find all School-related info fast with the new School-Specific MBA Forum

It is currently 18 Apr 2014, 23:24

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

ABCD is a rectangle ...

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 18 Sep 2010
Posts: 60
Followers: 2

Kudos [?]: 17 [0], given: 303

ABCD is a rectangle ... [#permalink] New post 16 Apr 2011, 23:04
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

40% (03:27) correct 60% (01:00) wrong based on 5 sessions
hello
i cant solve this geometry question :shock: , plz help!
tanx :oops:
[Reveal] Spoiler: OA

Attachments

geo.png
geo.png [ 24.52 KiB | Viewed 1784 times ]


_________________

(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

3 KUDOS received
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2058
Followers: 123

Kudos [?]: 827 [3] , given: 376

GMAT Tests User
Re: ABCD is a rectangle ... [#permalink] New post 16 Apr 2011, 23:36
3
This post received
KUDOS
annmary wrote:
hello
i cant solve this geometry question :shock: , plz help!
tanx :oops:


Sol:
Let l=length
w=wdith
d=diagonal=2
Area=l*w=l*\sqrt{d^2-l^2}

l*\sqrt{2^2-l^2}

l*\sqrt{4-l^2}=Area

Squaring both sides;
l^2*(4-l^2)=(Area)^2
4l^2-l^4=(Area)^2
-l^4+4l^2-(Area)^2=0

Let \hspace{2} l^2=x

-x^2+4x-(Area)^2=0

D=\sqrt{b^2-4*a*c}

D=\sqrt{4^2-4*(-1)*-(Area)^2}

D=\sqrt{16-4*(Area)^2}

In inside of the root must be greater or equal to 0 to provide valid roots of the equation.
16-4*(Area)^2 \ge 0

4*(Area)^2 \le 16

(Area)^2 \le 4

(Area) \le 2

Only I and II are less than 2.

Ans: "D"
_________________

~fluke

Manager
Manager
User avatar
Joined: 18 Sep 2010
Posts: 60
Followers: 2

Kudos [?]: 17 [0], given: 303

Re: ABCD is a rectangle ... [#permalink] New post 17 Apr 2011, 05:12
thank you fluke
your solution is very well.
+5 kudos , but i just can give you +1 kudos ;-)
other 4 kudos :+1,+1,+1,+1
_________________

(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

1 KUDOS received
Manager
Manager
Joined: 17 Jan 2011
Posts: 243
Followers: 1

Kudos [?]: 21 [1] , given: 4

GMAT Tests User
Re: ABCD is a rectangle ... [#permalink] New post 17 Apr 2011, 13:20
1
This post received
KUDOS
Area cannot be 3.2 because area of circle is pi r^2 i.e. 3.14, so rule out III
Even if the length is very close to the diameter i.e. 1 approx, width has to be 1/100 to make the area .01 - possible
similarly 1.9 is also possible.
=>D
_________________

Good Luck!!!

***Help and be helped!!!****

3 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 424
WE 1: Business Development
Followers: 6

Kudos [?]: 28 [3] , given: 161

GMAT ToolKit User GMAT Tests User
Re: ABCD is a rectangle ... [#permalink] New post 19 Apr 2011, 04:47
3
This post received
KUDOS
i did it a bit different.

Max size for a rectangle is a square.
and minimum is when the width or length = to 0 (or almost 0)

so lets check the max and than we know that everything below the max is a possibility.

so if we know the radii is 1 - we know that if it was a square its diagonals will be 2 each.
so the area of the rectangle will be < 2*2/2 = 2

so - I, II is below 2, above 0 - than - they are ok.
Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 424
WE 1: Business Development
Followers: 6

Kudos [?]: 28 [0], given: 161

GMAT ToolKit User GMAT Tests User
Re: ABCD is a rectangle ... [#permalink] New post 19 Apr 2011, 05:07
thanks old friend.
1 KUDOS received
Manager
Manager
Joined: 09 Jan 2010
Posts: 128
Followers: 1

Kudos [?]: 4 [1] , given: 12

Re: ABCD is a rectangle ... [#permalink] New post 01 May 2011, 19:10
1
This post received
KUDOS
area of rectangle = l*b

diagonal is 2
also d (diagonal) = sqrt (l^2 + b^2)
l*b = l * sqrt (2 -l^2)
area is positive
therefore (2-l^2) >0
i.e sqrt2>l
similarly sqrt2>b
therefore area = l.b <sqrt 2.sqrt2 = 1.4 *1.4 = 1.96
therefore D is correct.
1 KUDOS received
VP
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1368
Followers: 9

Kudos [?]: 121 [1] , given: 10

GMAT Tests User
Re: ABCD is a rectangle ... [#permalink] New post 01 May 2011, 21:29
1
This post received
KUDOS
Max area of the rectangle possible when diagonal = diameter = 2
Hence, l^2 + b^2 = 4. Implies l and b < 1.5 each.
Also, area of circle = 3.14 * 1^2 = 3.14. hence options C and E POE.
Now,
0<l <1.5 and 0<b<1.5. Thus area can be 0.01 and 1.9 both.
Hence D.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Re: ABCD is a rectangle ...   [#permalink] 01 May 2011, 21:29
    Similar topics Author Replies Last post
Similar
Topics:
New posts Experts publish their posts in the topic Is quadrilateral ABCD a rectangle? agnok 8 09 Sep 2010, 06:42
New posts Experts publish their posts in the topic What is the perimeter of rectangle ABCD ? jamifahad 8 29 Sep 2011, 05:05
New posts 1 What is the area of rectangle ABCD? dvinoth86 1 12 Sep 2012, 17:15
New posts Experts publish their posts in the topic Rectangle ABCD is divided into five identical rectangles. bagdbmba 6 05 Jul 2013, 00:43
New posts 1 Experts publish their posts in the topic Is quadrilateral ABCD a rectangle? mattce 1 16 Jul 2013, 18:23
Display posts from previous: Sort by

ABCD is a rectangle ...

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.