GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 05 Jul 2020, 22:58

### 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

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

# A rectangular photograph is surrounded by a border that is 1

Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 Nov 2008
Posts: 26
A rectangular photograph is surrounded by a border that is 1  [#permalink]

### Show Tags

Updated on: 29 Oct 2013, 02:33
8
91
00:00

Difficulty:

55% (hard)

Question Stats:

72% (02:48) correct 28% (03:00) wrong based on 884 sessions

### HideShow timer Statistics

A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?

A. 34
B. 36
C. 38
D. 40
E. 42

Originally posted by petercao on 09 Nov 2008, 19:19.
Last edited by Bunuel on 29 Oct 2013, 02:33, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 64951
Re: A rectangular photograph is surrounded by a border that is 1  [#permalink]

### Show Tags

29 Oct 2013, 02:43
7
39
petercao wrote:
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?

A. 34
B. 36
C. 38
D. 40
E. 42

Similar questions to practice about rectangles:
a-square-wooden-plaque-has-a-square-brass-inlay-in-the-89215.html
a-border-of-uniform-width-is-placed-around-a-rectangular-144434.html
a-rectangular-yard-is-20-yards-wide-and-40-yards-long-it-is-8453.html
the-figure-above-represents-a-square-plot-measuring-x-feet-o-160568.html

Similar questions to practice about circles:
marty-s-pizza-shop-guarantees-that-their-pizzas-all-have-a-148428.html
the-figure-above-shows-a-circular-flower-bed-with-its-cente-144448.html
_________________
SVP
Joined: 30 Apr 2008
Posts: 1534
Location: Oklahoma City
Schools: Hard Knocks

### Show Tags

09 Nov 2008, 19:46
33
20
D.

First, we know that M is the area of the picture AND the border, and that the border is 1 in wide. If you have a border around a picture that is 1" wide, it doesn't add just 1" to the width and height, but actually 2" to the width and 2" to the height because you have an extra inch on each side for the border.

So, if we want to let x = width of the photograph (no border) and y = height of the photograph (no border), then we know that M = (border width + photograph width) * (border + photograph height).

A border adds twice its width to the width of the photograph. A 4" picture will have a 1" border on the right and left, so it adds 2", for a new width of 6". (Hypothetical example). For a 2" wide border, the added dimensions will be twice the width of the border, or 4" (2" for each left and right side).

(x+4)(y+4) = M + 52

But we know that M is the area of the photograph plus a 1" border. This is represented alegbraically like:

(x+2)(y+2) = M

So substitute in:

(x+4)(y+4) = (x+2)(y+2) + 52, Now lets reduce as far as we can. First do FOIL.

xy + 4x + 4y + 16 = xy + 2x +2y +4 +52

The xy on each side cancels each other out.

4x + 4y + 16 = 2x + 2y + 56
subtract the following values from each side: 2x, 2y and 16

2x + 2y = 40.

We can reduce further if you want to, but it isn't necessary.

If you have a rectangle with height (x) and width (y) and you want to find the perimeter, then you can do x + x + y + y = perimter. Also known as 2x + 2y = Perimeter.

This shows us that the perimter should be 40.

petercao wrote:
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?

A. 34
B. 36
C. 38
D. 40
E. 42
##### General Discussion
Intern
Joined: 07 Nov 2008
Posts: 22

### Show Tags

09 Nov 2008, 19:54
8
7
petercao wrote:
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?

A. 34
B. 36
C. 38
D. 40
E. 42

width = x, height = y,
2x+2y=?

(x+4)(y+4)-(x+2)(y+2)=M+52-M
2x+2y=40

D
Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 311
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB

### Show Tags

17 Aug 2010, 20:28
Sion wrote:
petercao wrote:
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?

A. 34
B. 36
C. 38
D. 40
E. 42

width = x, height = y,
2x+2y=?

(x+4)(y+4)-(x+2)(y+2)=M+52-M
2x+2y=40

D

Agreed.

Outer rectangle area when width is two inches on either side - Outer rectangle area when the width is 1 inch
= M + 52 - M.

2 (l+b) = 40 units.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1706
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A rectangular photograph is surrounded by a border that is 1  [#permalink]

### Show Tags

29 Oct 2013, 02:27
24
2
Attachments

jo.JPG [ 21.87 KiB | Viewed 85002 times ]

Intern
Joined: 23 Dec 2014
Posts: 47
Re: A rectangular photograph is surrounded by a border that is 1  [#permalink]

### Show Tags

25 Jan 2015, 03:08
I did not understand how 1 inch border is counted as 2. Can somebody please explain?
Math Expert
Joined: 02 Sep 2009
Posts: 64951
Re: A rectangular photograph is surrounded by a border that is 1  [#permalink]

### Show Tags

25 Jan 2015, 03:12
Salvetor wrote:
I did not understand how 1 inch border is counted as 2. Can somebody please explain?

1 inch from right and left sides of the photograph give 2 inches. Similarly 1 inch from top and bottom of the photograph give 2 inches.
_________________
Manager
Joined: 27 Oct 2013
Posts: 196
Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
A rectangular photograph is surrounded by a border that is 1  [#permalink]

### Show Tags

25 Jan 2015, 05:40
1
1
Here we go----

Let Length and Breadth of photograph be L and B respectively.
Perimeter is given by 2*(L+b) -----(1)

According to the question:

(L+2)(B+2) = m ----(2)

and

(L+4)(B+4) = m + 52 ---------> (L+4)(B+4) - 52 = m ------(3)

Equating (2) and (3)

(L+2)(B+2) = (L+4)(B+4) - 52

LB + 2L + 2B + 4 = LB + 4L + 4B + 16 -52

Simplify
2L + 2B = 40 ------> 2(L+B) = 40 (Check eq (1))

Director
Joined: 23 Jan 2013
Posts: 505
Schools: Cambridge'16
Re: A rectangular photograph is surrounded by a border that is 1  [#permalink]

### Show Tags

25 Jan 2015, 23:57
x*y=M

(x+2)*(y+2)=M+52, because every 1 inch in side gives additional 2 inches in lenght

2x+2y+4=52

2(x+y)=48, it is perimeter with border

48-8=40, where 8 is total lenght of border sides

D
Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 805
Location: United States (CA)
Age: 40
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GMAT 4: 730 Q48 V42 (Online)
GRE 1: Q168 V169
WE: Education (Education)
Re: A rectangular photograph is surrounded by a border that is 1  [#permalink]

### Show Tags

26 Jul 2015, 09:12
Attachments

File comment: Here is a visual that might help. Notice how I'm plugging in lengths and widths to make the prompt true: usually we plug in constants, but it's a good example of how you can even plug in variables.

Screen Shot 2015-07-26 at 10.09.22 AM.png [ 167.72 KiB | Viewed 75871 times ]

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11036
Location: United States (CA)
Re: A rectangular photograph is surrounded by a border that is 1  [#permalink]

### Show Tags

28 Apr 2017, 13:58
5
2
petercao wrote:
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?

A. 34
B. 36
C. 38
D. 40
E. 42

We are given that a rectangular photograph is surrounded by a border that is 1 inch wide on each side and that the total area of the photograph and border is M square inches. If we let L = the length of the photograph and W = the width of the photograph, since the border surrounds the length and width on two sides, the length of the photograph and border is L + 2 and the width of the photograph and border is W + 2.

Let’s represent this in a diagram:

We can now represent the area of the border and photograph:

area = length x width

M = (L + 2)(W + 2)

M = WL + 2W + 2L + 4

We are also given that if the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. Thus, the new length of the border and photograph would be L + 4 and the new width of the border and photograph would be W + 4.

We can again represent this in a diagram:

The new area of the border and photograph is:

M + 52 = (L + 4)(W + 4)

M + 52 = WL + 4W + 4L + 16

M = WL + 4W + 4L – 36

We have two equations for M. Let’s equate them and simplify:

WL + 2W + 2L + 4 = WL + 4W + 4L – 36

2W + 2L + 4 = 4W + 4L – 36

2W + 2L = 4W + 4L – 40

2W + 2L = 40

Since perimeter = 2L + 2W, the perimeter of the photograph is 40 inches.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
225 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Senior Manager
Joined: 29 Jun 2017
Posts: 411
GPA: 4
WE: Engineering (Transportation)
A rectangular photograph is surrounded by a border that is 1  [#permalink]

### Show Tags

14 Aug 2017, 02:14
LB=M
(L+2)(B+2) = M+52
2(L+B) = 48
Perimeter of pic = 2x (L-2+B-2) = 2(L+B)-8 = 48-8 =40

Math Expert
Joined: 02 Aug 2009
Posts: 8753
Re: A rectangular photograph is surrounded by a border that is 1  [#permalink]

### Show Tags

16 Jul 2018, 21:49
petercao wrote:
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?

A. 34
B. 36
C. 38
D. 40
E. 42

You can get a quick solution geometrically...
The area of just outer boundary is M+52-M=52..
Draw a line (red) to divide this boundary into 4 parts..
1) 2 parts are rectangle with sides (X+4) and 1
So area = $$(X+4)*1=X+4$$... Area of both parts = $$2(X+4)=2x+8$$
2) 2 parts are rectangle with sides (y+2) and 1
So area = $$(y+2)*1=y+2$$......area of both parts =$$2(y+2)=2y+4$$

Total area =$$52=2x+8+2y+4=2x+2y=12.$$..
So $$2x+2y=52-12=40........2(X+y)=40$$
2(X+y) is nothing but the perimeter of photograph.
Hence Ans 40
Attachments

PicsArt_07-17-09.04.48.jpg [ 49.14 KiB | Viewed 35399 times ]

_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 15382
Re: A rectangular photograph is surrounded by a border that is 1  [#permalink]

### Show Tags

24 Jul 2019, 02:20
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.
_________________
Re: A rectangular photograph is surrounded by a border that is 1   [#permalink] 24 Jul 2019, 02:20