December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 04 Aug 2010
Posts: 13

A rectangular picture is surrounded by a boarder, as shown in the
[#permalink]
Show Tags
Updated on: 11 Feb 2018, 21:23
Question Stats:
72% (02:23) correct 28% (02:46) wrong based on 232 sessions
HideShow timer Statistics
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 Attachment:
Rectangular.jpg [ 11.23 KiB  Viewed 10528 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by kwhitejr on 17 Aug 2010, 17:21.
Last edited by Bunuel on 11 Feb 2018, 21:23, edited 2 times 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: 363
Location: Milky way
Schools: ISB, Tepper  CMU, Chicago Booth, LSB

Re: A rectangular picture is surrounded by a boarder, as shown in the
[#permalink]
Show Tags
17 Aug 2010, 17:54
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: 22
Schools: SUNY at Stonyb Brook
WE 1: 4 yrs

Re: A rectangular picture is surrounded by a boarder, as shown in the
[#permalink]
Show Tags
17 Aug 2010, 18:15
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: 12 Aug 2012
Posts: 6

Re: A rectangular picture is surrounded by a boarder, as shown in the
[#permalink]
Show Tags
26 Jul 2013, 22:37
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: 1825
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: A rectangular picture is surrounded by a boarder, as shown in the
[#permalink]
Show Tags
29 Oct 2013, 02:02
Please refer fig below:
Attachments
Rectangular.jpg [ 21.25 KiB  Viewed 9371 times ]
_________________
Kindly press "+1 Kudos" to appreciate



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13087
Location: United States (CA)

Re: A rectangular picture is surrounded by a boarder, as shown in the
[#permalink]
Show Tags
03 Jun 2015, 14:48
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
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8678
Location: Pune, India

Re: A rectangular picture is surrounded by a boarder, as shown in the
[#permalink]
Show Tags
03 Jun 2015, 20:26
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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 21 May 2015
Posts: 232
Concentration: Operations, Strategy

Re: A rectangular picture is surrounded by a boarder, as shown in the
[#permalink]
Show Tags
03 Jun 2015, 23:37
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: 165
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 in the
[#permalink]
Show Tags
07 Jun 2015, 02:47
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: 8678
Location: Pune, India

Re: A rectangular picture is surrounded by a boarder, as shown in the
[#permalink]
Show Tags
08 Jun 2015, 06:56
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 7333 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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 417
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

Re: A rectangular picture is surrounded by a boarder, as shown in the
[#permalink]
Show Tags
23 Jun 2015, 05:10
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 7147 times ]



BSchool Forum Moderator
Joined: 23 May 2018
Posts: 289
Location: Pakistan
GPA: 3.4

Re: A rectangular picture is surrounded by a boarder, as shown in the
[#permalink]
Show Tags
06 Oct 2018, 12:10
kwhitejr wrote: 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 Attachment: Rectangular.jpg Let \(x\) be the width and \(2x\) the length of the photo. Therefore, the width of the frame is \(x+4\) and the length is \(2x+4\) Area of Frame & Photo  Area of Photo = Area of Frame \((2x+4)*(x+4)2x^2=196\) \(2x(x+4)+4(x+4)2x^2=196\) \(2x^2+8x+4x+162x^2=196\) \(12x=19616\) \(12x=180\) \(x=\frac{180}{12}\) \(x=15\) Length of the photo \(= 2x = 30 inches\)
_________________
If you can dream it, you can do it.
Practice makes you perfect.
Kudos are appreciated.




Re: A rectangular picture is surrounded by a boarder, as shown in the &nbs
[#permalink]
06 Oct 2018, 12:10






