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

It is currently 18 Jul 2018, 09:01

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.

Close

Request Expert Reply

Confirm Cancel

A rectangular photograph is surrounded by a border that is 1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

6 KUDOS received
Intern
Intern
avatar
Joined: 08 Nov 2008
Posts: 29
A rectangular photograph is surrounded by a border that is 1 [#permalink]

Show Tags

New post Updated on: 29 Oct 2013, 03:33
6
38
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

77% (01:41) correct 23% (02:49) wrong based on 866 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, 20:19.
Last edited by Bunuel on 29 Oct 2013, 03:33, edited 1 time in total.
Added the OA.
Most Helpful Expert Reply
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47080
Re: A rectangular photograph is surrounded by a border that is 1 [#permalink]

Show Tags

New post 29 Oct 2013, 03:43
2
15
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
a-circular-lawn-with-a-radius-of-5-meters-is-surrounded-by-a-154737.html
the-figure-above-shows-a-circular-flower-bed-with-its-cente-144448.html
the-figure-shows-the-top-side-of-a-circular-medallion-made-o-101845.html
_________________

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

Most Helpful Community Reply
15 KUDOS received
SVP
SVP
User avatar
Joined: 30 Apr 2008
Posts: 1841
Location: Oklahoma City
Schools: Hard Knocks
Re: rectangular--28 [#permalink]

Show Tags

New post 09 Nov 2008, 20:46
15
13
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

_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

GMAT Club Premium Membership - big benefits and savings

General Discussion
8 KUDOS received
Intern
Intern
User avatar
Joined: 07 Nov 2008
Posts: 29
Re: rectangular--28 [#permalink]

Show Tags

New post 09 Nov 2008, 20:54
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
Senior Manager
User avatar
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 384
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: rectangular--28 [#permalink]

Show Tags

New post 17 Aug 2010, 21:28
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.
_________________

:good Support GMAT Club by putting a GMAT Club badge on your blog :thanks

17 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
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

New post 29 Oct 2013, 03:27
17
2
Please refer below:
Attachments

jo.JPG
jo.JPG [ 21.87 KiB | Viewed 49636 times ]


_________________

Kindly press "+1 Kudos" to appreciate :)

Intern
Intern
avatar
B
Joined: 23 Dec 2014
Posts: 48
Re: A rectangular photograph is surrounded by a border that is 1 [#permalink]

Show Tags

New post 25 Jan 2015, 04:08
I did not understand how 1 inch border is counted as 2. Can somebody please explain?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47080
Re: A rectangular photograph is surrounded by a border that is 1 [#permalink]

Show Tags

New post 25 Jan 2015, 04:12
1 KUDOS received
Manager
Manager
avatar
Joined: 27 Oct 2013
Posts: 232
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

New post 25 Jan 2015, 06:40
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))

Answer is D
Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 598
Schools: Cambridge'16
Re: A rectangular photograph is surrounded by a border that is 1 [#permalink]

Show Tags

New post 26 Jan 2015, 00:57
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
Director
User avatar
G
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 657
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: Q168 V169
WE: Education (Education)
Re: A rectangular photograph is surrounded by a border that is 1 [#permalink]

Show Tags

New post 26 Jul 2015, 10:12
Please see attached visual.
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
Screen Shot 2015-07-26 at 10.09.22 AM.png [ 167.72 KiB | Viewed 40450 times ]


_________________

Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both in-person (San Diego, CA, USA) and online worldwide, since 2002.

One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).

You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y94hlarr Date of Birth: 09 December 1979.

GMAT Action Plan and Free E-Book - McElroy Tutoring

Contact: mcelroy@post.harvard.edu

Expert Post
2 KUDOS received
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2928
Location: United States (CA)
Re: A rectangular photograph is surrounded by a border that is 1 [#permalink]

Show Tags

New post 28 Apr 2017, 14:58
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:

Image

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:

Image

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.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 497
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
A rectangular photograph is surrounded by a border that is 1 [#permalink]

Show Tags

New post 14 Aug 2017, 03:14
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

Answer is D
_________________

Give Kudos for correct answer and/or if you like the solution.

Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6233
Re: A rectangular photograph is surrounded by a border that is 1 [#permalink]

Show Tags

New post 16 Jul 2018, 22:49
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
PicsArt_07-17-09.04.48.jpg [ 49.14 KiB | Viewed 148 times ]


_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Re: A rectangular photograph is surrounded by a border that is 1   [#permalink] 16 Jul 2018, 22:49
Display posts from previous: Sort by

A rectangular photograph is surrounded by a border that is 1

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

Events & Promotions

PREV
NEXT


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®.