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

It is currently 13 Dec 2018, 23:49

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar

Photo Frame Perimeter Question

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 16 Jul 2018
Posts: 1
Photo Frame Perimeter Question  [#permalink]

Show Tags

New post 16 Jul 2018, 18:29
I am struggling to break through this question and have revisited over multiple days. Any help would be appreciated.

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?
Director
Director
User avatar
G
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 610
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: Photo Frame Perimeter Question  [#permalink]

Show Tags

New post 16 Jul 2018, 18:57
Top Contributor
Let the dimensions of the photograph be L*B (L is length and B is breadth)

The photograph has 1 inch wide border on each side so in the dimension of the photograph and the border (1 inch on each side) will become (L+1+1) * (B+1+1) (See attached figure)
So Area = (L+2) * (B+2) = M (Given) ...(1)

Similarly when the Border is 2 inch on each side then Area will become (L+2+2) * (B+2+2) (see attached figure)
=> (L+4) * (B+4) = M + 52 (Given) ...(2)
[(L+2) + 2] * [(B+2) + 2] = M + 52
(L+2)*(B+2) + 2*(L+2) + 2(B+2) + 2*2 = M + 52
(L+2) * (B+2) = M from 1
=> M + 2* (L+2 + B+2) + 4 = M+52
=> 2*(L+B+4) = M + 52 - M - 4
=> 2(L+B+4) = 48
=> L + B + 4 = 24
=> L + B = 20
So, Perimeter = 2*(L+B) = 2*20 = 40 inches

Hope it helps!

More discussion here

Chelsann15 wrote:
I am struggling to break through this question and have revisited over multiple days. Any help would be appreciated.

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?

Attachments

image.JPG
image.JPG [ 52.56 KiB | Viewed 250 times ]


_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7106
Photo Frame Perimeter Question  [#permalink]

Show Tags

New post 16 Jul 2018, 19:43
Chelsann15 wrote:
I am struggling to break through this question and have revisited over multiple days. Any help would be appreciated.

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?



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

Hope it helps
Attachments

PicsArt_07-17-09.04.48.jpg
PicsArt_07-17-09.04.48.jpg [ 49.14 KiB | Viewed 236 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

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6635
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Photo Frame Perimeter Question  [#permalink]

Show Tags

New post 18 Jul 2018, 07:42
Chelsann15 wrote:
I am struggling to break through this question and have revisited over multiple days. Any help would be appreciated.

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?


Let \(l\) and \(w\) be the length and the width of the photograph.
From the condition we have \((l+2)(w+2) = lw + 2l + 2w + 4 = M\).
We also have \((l+4)(w+4) = lw + 4l + 4w + 16 = M + 52\).
Then \((lw + 4l + 4w + 16 ) - (lw + 2l + 2w + 4) = 2l + 2w + 12 = (M+52)- M\).
\(2(l+w) = 40\)
Here \(2(l+w)\) is the perimeter of the photography.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

GMAT Club Bot
Re: Photo Frame Perimeter Question &nbs [#permalink] 18 Jul 2018, 07:42
Display posts from previous: Sort by

Photo Frame Perimeter Question

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

Moderator: souvonik2k



cron
Copyright

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®.