Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 04 Aug 2010
Posts: 14

A rectangular picture is surrounded by a boarder, as shown [#permalink]
Show Tags
17 Aug 2010, 18:21
4
This post was BOOKMARKED
Question Stats:
74% (03:31) correct
26% (03:10) wrong based on 179 sessions
HideShow timer Statistics
Attachment:
Rectangular.jpg [ 11.23 KiB  Viewed 5954 times ]
A rectangular picture is surrounded by a boarder, as shown in the figure above. Without the boarder the length of the picture is twice its width. If the area of the boarder is 196 square inches, what is the length, in inches, of the picture, excluding the boarder? A. 10 B. 15 C. 30 D. 40 E. 60
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 25 Jul 2013, 02:59, edited 1 time in total.
Renamed the topic, edited the question, added the OA and the image.



Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 408
Location: Milky way
Schools: ISB, Tepper  CMU, Chicago Booth, LSB

Re: Determining Area [#permalink]
Show Tags
17 Aug 2010, 18:54
kwhitejr wrote: FIGURE: Imagine a rectangle within a rectangle. Every side of the interior rectangle is 2 inches from the congruous side of the larger rectangle.
A rectangular picture is surrounded by a border, as shown in the figure above. Without the border the length of the picture is twice the width. If the area of the border is 196 square inches, what is the length, in inches, of the picture, excluding the border?
A. 10 B. 15 C. 30 D. 40 E. 60 Answer : 30. Length of the outer rectangle  L, Breadth of the outer rectangle  B. Length of the inner rectangle  l, Breadth of the inner rectangle  b. Now given that  L*B = 196 sq. unit and l = 2b. Also l = L  4 and b = B  4 Hence area of the outer rectangle (border area) = 196  Area of the inner rectangle (L * B) = 196  (l*b) ((l+4) * (b+4)) = 196  (l*b) Simplifying => (lb + 4l + 4b + 16) = (196  lb) (4l + 4b) = 180 (4(2b) + 4b) = 180 12b = 180 b = 15, l = 30. Hence the length of the inner rectangle or picture is 30 units. Answer C.
_________________
Support GMAT Club by putting a GMAT Club badge on your blog



Intern
Joined: 11 Aug 2010
Posts: 23
Schools: SUNY at Stonyb Brook
WE 1: 4 yrs

Re: Determining Area [#permalink]
Show Tags
17 Aug 2010, 19:15
1
This post was BOOKMARKED
Ans : C Assume the length of inner rectangle as L and the width as w then L = 2W so the length of outer rectange will be L+4 and width as W+4 The area of border is area of outer rectangle  area of inner rectangle [(L+4)*(W+4)] [ L * W] =196 4L +4W +16 = 196 substituting L = 2W we get 12W = 180 W= 15 L = 2W = 30
_________________
Consider giving Kudos if my post helped you in some way



Intern
Joined: 26 Sep 2012
Posts: 17

Re: Determining Area [#permalink]
Show Tags
25 Jul 2013, 02:55
1
This post received KUDOS
How to attach a picture to the first post?
Attachments
Rectangular.jpg [ 11.23 KiB  Viewed 5884 times ]



Math Expert
Joined: 02 Sep 2009
Posts: 39626

Re: Determining Area [#permalink]
Show Tags
25 Jul 2013, 03:00



Intern
Joined: 12 Aug 2012
Posts: 7

Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
Show Tags
26 Jul 2013, 23:37
In border area there are 4 square , two simillar rectangle and two another similar rectangle L= length of inner rectangle, l= width of inner rectangle Given L= 2l , Border area 196= 4 square ( 2*2) + 2 rectangle (2*l)+ 2 rectangle (2*L) 196= 16+ 2*L+ 2*L + L/2*2+L/2*2 180=6L L= 30. Hope the approach is correct Regards,



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
Show Tags
29 Oct 2013, 03:02
4
This post received KUDOS
Please refer fig below:
Attachments
Rectangular.jpg [ 21.25 KiB  Viewed 5446 times ]
_________________
Kindly press "+1 Kudos" to appreciate



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15939

Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
Show Tags
01 Jun 2015, 23:00
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 9257
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
Show Tags
03 Jun 2015, 15:48
Hi All, Many Test Takers would use an algebraic approach to solving this problem (which is fine). Since the prompt asks for the length of the picture and the answer are NUMBERS, we can TEST THE ANSWERS. We're given some facts to work with: 1) The length of the picture is TWICE its width 2) The area of the BORDER is 196 sq. inches 3) The border "adds 4" to the length and width of the picture We're asked for the LENGTH of the picture. Since the Length is TWICE the width, chances are that we're looking for an answer that is TWICE another answer (which means either 30 & 15 or 60 & 30). Let's TEST Answer C: 30 IF..... Length = 30 Width = 15 Area of picture = 450 Total Length = 34 Total Width = 19 Total area = 646 Total area  picture area = 646  450 = 196. This is a MATCH for what we were told, so this MUST be the answer. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
Show Tags
03 Jun 2015, 21:26
kwhitejr wrote: Attachment: Rectangular.jpg A rectangular picture is surrounded by a boarder, as shown in the figure above. Without the boarder the length of the picture is twice its width. If the area of the boarder is 196 square inches, what is the length, in inches, of the picture, excluding the boarder? A. 10 B. 15 C. 30 D. 40 E. 60 Here is a 20 second estimation method: Say the width of the picture is b. Area of the frame can be approximated to 2*b + 2*b + 2*2b + 2*2b = 12b. Some area is left out here. Ignore it. 12b is a bit less than 196 so b would be more than 10 but less than 20. So length is more than 20 but less than 40. The only option is (C) Alternatively, if you want to find the exact value, the area of the left out region is 4 squares of 2*2 i.e. 16 square inches. So 12b = 196  16 = 180 b = 15 So length = 30
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Senior Manager
Joined: 21 May 2015
Posts: 271
Concentration: Operations, Strategy

Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
Show Tags
04 Jun 2015, 00:37
C (l+4) (b+4)  lb = 196 l+b = 45 if l=2b then b=15 and l=30
_________________
Apoorv
I realize that i cannot change the world....But i can play a part



Manager
Joined: 11 Aug 2011
Posts: 195
Location: United States
Concentration: Economics, Finance
Schools: Booth '17, Sloan '17, CBS '17, Ross '17 (S), Haas '17, Stern '17, Yale '17, Anderson '17, Kelley '17 (S), KenanFlagler '17 (S), HEC Dec '17, HKUST '16, Jones '16, NUS '17
GMAT Date: 10162013
GPA: 3
WE: Analyst (Computer Software)

Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
Show Tags
07 Jun 2015, 03:47
VeritasPrepKarishma wrote: kwhitejr wrote: Attachment: Rectangular.jpg A rectangular picture is surrounded by a boarder, as shown in the figure above. Without the boarder the length of the picture is twice its width. If the area of the boarder is 196 square inches, what is the length, in inches, of the picture, excluding the boarder? A. 10 B. 15 C. 30 D. 40 E. 60 Here is a 20 second estimation method: Say the width of the picture is b. Area of the frame can be approximated to 2*b + 2*b + 2*2b + 2*2b = 12b. Some area is left out here. Ignore it. 12b is a bit less than 196 so b would be more than 10 but less than 20. So length is more than 20 but less than 40. The only option is (C) Alternatively, if you want to find the exact value, the area of the left out region is 4 squares of 2*2 i.e. 16 square inches. So 12b = 196  16 = 180 b = 15 So length = 30 Hi karishma, I did not understand how you can approximate area of the frame as 2*b + 2*b + 2*2b + 2*2b = 12b. Can you please explain this in detail.
_________________
Kudos me if you like my post !!!!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
Show Tags
08 Jun 2015, 07:56
akhil911 wrote: VeritasPrepKarishma wrote: kwhitejr wrote: Attachment: The attachment Rectangular.jpg is no longer available A rectangular picture is surrounded by a boarder, as shown in the figure above. Without the boarder the length of the picture is twice its width. If the area of the boarder is 196 square inches, what is the length, in inches, of the picture, excluding the boarder? A. 10 B. 15 C. 30 D. 40 E. 60 Here is a 20 second estimation method: Say the width of the picture is b. Area of the frame can be approximated to 2*b + 2*b + 2*2b + 2*2b = 12b. Some area is left out here. Ignore it. 12b is a bit less than 196 so b would be more than 10 but less than 20. So length is more than 20 but less than 40. The only option is (C) Alternatively, if you want to find the exact value, the area of the left out region is 4 squares of 2*2 i.e. 16 square inches. So 12b = 196  16 = 180 b = 15 So length = 30 Hi karishma, I did not understand how you can approximate area of the frame as 2*b + 2*b + 2*2b + 2*2b = 12b. Can you please explain this in detail. Attachment:
Approx Area.jpg [ 332.5 KiB  Viewed 3418 times ]
The shaded region is approximately 2b + 2b + 4b + 4b. The four little squares (with question marks) is the only area unaccounted for.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 441
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
Show Tags
23 Jun 2015, 06:10
1
This post received KUDOS
Hey, I started with calculating the area of the frame. The small corners (red rectangles): We know that the frame is 2 wide from every side. So each of the red rectangles will have an area of 2^2 = 4. We have four of those, so 4*4 = 16. The green rectangles: 2*2w = 4w. We have two of those, so 2*4w = 8w. The black (remaining two rectangles): 2*w = 2w. We have two of those, so 2*2w = 4w. Adding the different areas gives as the total frame area: 16 + 12w From the stem we know that 16 + 12w = 196. So, w = 15 and the length is 30.
Attachments
frame.png [ 5.87 KiB  Viewed 3257 times ]



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15939

Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
Show Tags
16 Aug 2016, 20:29
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: A rectangular picture is surrounded by a boarder, as shown
[#permalink]
16 Aug 2016, 20:29







