Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 18 Jul 2019, 06:20

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 photo has a 2mm thick frame uniformly around it. If the

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

Hide Tags

Find Similar Topics 
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1230
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
A rectangular photo has a 2mm thick frame uniformly around it. If the  [#permalink]

Show Tags

New post 24 Nov 2018, 10:08
1
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

50% (03:02) correct 50% (02:59) wrong based on 22 sessions

HideShow timer Statistics


GMATbuster's Weekly Quant Quiz#10 Ques #4


For Questions from earlier quizzes: Click Here


A rectangular photo has a 2mm thick frame uniformly around it. If the frame size is reduced to 1 mm, the total area of the photograph with the frame is reduced by 20 mm^2. If the length and breadth of the photograph are integers and if the length is greater than breadth, find the ratio of the length and breadth of the photograph including the original frame.
A) 6/5
B) 7/5
C) 5/3
D) 2/1
E) 3/1

_________________
Intern
Intern
avatar
B
Joined: 07 Nov 2018
Posts: 9
Re: A rectangular photo has a 2mm thick frame uniformly around it. If the  [#permalink]

Show Tags

New post 24 Nov 2018, 10:16
Answer E, from given info l+b = 4, and since l>b, l=3, b=1
Manager
Manager
User avatar
P
Joined: 09 Jun 2018
Posts: 191
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: A rectangular photo has a 2mm thick frame uniformly around it. If the  [#permalink]

Show Tags

New post 24 Nov 2018, 10:25
1
Let L be length and B be breadth, given that L and B are integers and L > B.
Original frame will have length = L + 2 + 2 = L + 4 and breadth = B + 2 + 2 = B + 4
Smaller frame will have length = L + 1 + 1 = L + 2 and breadth = B + 1 + 1 = B + 2

So, as per condition given in question:
(L + 4)*(B + 4) - (L + 2)*(B + 2) = 20
LB + 4B + 4L + 16 - LB - 2B - 2L - 4 = 20
2*(L + B) + 12 = 20
L + B = 4
Now, possible combinations of integers for L and B can be 1 + 3 = 4, 2 + 2 = 4 or 3 + 1 = 4.
But it is given that L > B, so only case possible is 3 + 1 = 4. Hence L = 3 and B = 1

Ratio asked = (L + 4) / (B + 4) = (3+4)/(1+4) = 7/5

IMO Option B! Is there a shortcut though?
_________________
If you found this relevant and useful, please Smash that Kudos button!
Intern
Intern
avatar
B
Joined: 07 Dec 2016
Posts: 10
Re: A rectangular photo has a 2mm thick frame uniformly around it. If the  [#permalink]

Show Tags

New post 24 Nov 2018, 10:45
E.
Original Area =(X+4)*(Y+4)
since thickness of frame will add on to both sides.

New thickness = (X+2)*(Y+2)

subtracting both :
2X + 2Y +12 =20
X+Y =4

Now since its given length is more so L=3 and B=1

So option E
X+Y

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 11 Nov 2016
Posts: 14
Re: A rectangular photo has a 2mm thick frame uniformly around it. If the  [#permalink]

Show Tags

New post 24 Nov 2018, 11:03
Let photograph be LxB
Thus
(L+4)(B+4)-(L+2)(B+2)=20
2(L+B)+12= 20
L+B= 4
Since both are integers and L>B thus L=3, B= 1
Hence ratio=3:1

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 11 Apr 2017
Posts: 20
Re: A rectangular photo has a 2mm thick frame uniformly around it. If the  [#permalink]

Show Tags

New post 24 Nov 2018, 11:25
gmatbusters wrote:

GMATbuster's Weekly Quant Quiz#10 Ques #4


For Questions from earlier quizzes: Click Here


A rectangular photo has a 2mm thick frame uniformly around it. If the frame size is reduced to 1 mm, the total area of the photograph with the frame is reduced by 20 mm^2. If the length and breadth of the photograph are integers and if the length is greater than breadth, find the ratio of the length and breadth of the photograph including the original frame.
A) 6/5
B) 7/5
C) 5/3
D) 2/1
E) 3/1


Let the length of photo be x
Let the breadth of photo be y
Area of photo -xy
Photo has a frame of 2 mm thick around it ,making the length as (x+4) and breadth (y+4)
Area of photo with frame-(x+4)(y+4)
Now the frame size is reduced to 1mm ,making the new area of photo with frame as (x+2)(y+2)
The total area of the photo with frame has been reduced to 20mm2
(x+4)(y+4)-20=(x+2)(y+2)
Solving tbe above equation will refuce to 2x+2y=8
x+y=4
y= 4-x
The ration of length to breadth becomes x/4-x
Checking all the options ,only option E satisty the above equation
There answer is 3/1(E)


Sent from my iPhone using GMAT Club Forum mobile app
Manager
Manager
avatar
S
Joined: 08 Jan 2013
Posts: 105
Re: A rectangular photo has a 2mm thick frame uniformly around it. If the  [#permalink]

Show Tags

New post 24 Nov 2018, 14:41
Area of uniform rectangular photo frame with length l, breadth b and width w is given by (l+2w)(b+2w) ............... (I)

Difference in area of photo of width 2mm and photo of width 1mm = 20 mm^2 ............. Given ................ (II)

Using (I) and (II), (l+4)(b+4) - (l+2)(b+2) = 20
that is, lb + 4l + 4b + 16 - lb - 2l - 2b - 4 = 20
that is, 2l + 2b = 8
that is, l + b = 4 ........... (III)

Length and breadth both are integers and length is greater than breadth ............. Given ........ (IV)

Using (III) and (IV), only possible values of length and breadth are 3 and 1 respectively.

We need to find ratio of length and breadth along with original frame,

So, Ratio = (3+2*2)/(1+2*2) = 7/5.

Hence, B is the correct answer.
GMAT Club Bot
Re: A rectangular photo has a 2mm thick frame uniformly around it. If the   [#permalink] 24 Nov 2018, 14:41
Display posts from previous: Sort by

A rectangular photo has a 2mm thick frame uniformly around it. If the

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne