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605-655 (Medium)|   Geometry|      
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Bunuel
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The front face of a square computer monitor consists of a square compu 21 Oct 2020, 00:15
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The front face of a square computer monitor consists of a square computer screen surrounded by a square frame. The monitor is advertised as 22 inches along the diagonal, including the frame. How big is the screen, measured along the diagonal?

(1) The frame comprises 1/11 of the side length of the monitor.

(2) The area of the frame alone is 42
 
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The front face of a square computer monitor consists of a square compu 21 Oct 2020, 01:15
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Bunuel
The front face of a square computer monitor consists of a square computer screen surrounded by a square frame. The monitor is advertised as 22 inches along the diagonal, including the frame. How big is the screen, measured along the diagonal?

(1) The frame comprises 1/11 of the side length of the monitor.

(2) The area of the frame alone is 42


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It is a data sufficiency question so try and establish the sufficiency without actually calculating anything. You have a square frame and inside that, a square screen. The good thing about squares is that the moment you have one bit of data about them, you can calculate anything. Say, if you have any one of diagonal, side, area and perimeter, you can get all the other three.

Say the outside length of the frame is F and the inside length i.e. length of the side of the screen is S.

You know the diagonal of the bigger square so you can get F easily. Diagonal = \(\sqrt{2}\)*Side

So you have the side length, F, of the full monitor.

Question: What is the length of the diagonal of the screen? If you get S, you can easily get Diagonal which is given by the relation shown above. So all you need to know is S.

(1) The frame comprises 1/11 of the side length of the monitor.
Out of F, 1/11 is frame length and 10/11 is screen length. Once you have F, you can get S. Sufficient

(2) Area of frame alone is 42.
We know the total area = \(F^2\)
\(F^2 - S^2 = 42\)
Since we know F, we will get a single value for S (since S cannot be negative). Sufficient.
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The front face of a square computer monitor consists of a square compu 21 Oct 2020, 06:08
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Bunuel
The front face of a square computer monitor consists of a square computer screen surrounded by a square frame. The monitor is advertised as 22 inches along the diagonal, including the frame. How big is the screen, measured along the diagonal?

(1) The frame comprises 1/11 of the side length of the monitor.

(2) The area of the frame alone is 42
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diagonal_sqr = sideV2
diagonal_monitor = 22
side_monitor: xV2=22, x=22/V2

(1) sufic
side_monitor=side_frame+side_screen
22/v2=1/11(22/v2)+side_screen

(2) sufic
area_fr = area_monitor-area_screen
42=(22/V2)^2-area_screen
finding area_screen, gets you side_screen

ans (D)
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The front face of a square computer monitor consists of a square compu 21 Oct 2020, 11:54
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The front face of a square computer monitor consists of a square computer screen surrounded by a square frame. The monitor is advertised as 22 inches along the diagonal, including the frame. How big is the screen, measured along the diagonal?

(1) The frame comprises 1/11 of the side length of the monitor.



side of the screen + frame = full monitor

X + 1/11* x = full monitor

Diagonal is already given as 22

X can be found using diagonal formulae

With x alone we can find diagonal of screen

(2) The area of the frame alone is 42

Area of whole monitor - area of Screen = area of frame

With diagonal as 22 area of monitor can be found

Hence area of screen can be found too

Using area of screen the diagonal can be found

Hence IMO D
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The front face of a square computer monitor consists of a square compu 25 Aug 2021, 08:00
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Bunuel
The front face of a square computer monitor consists of a square computer screen surrounded by a square frame. The monitor is advertised as 22 inches along the diagonal, including the frame. How big is the screen, measured along the diagonal?

(1) The frame comprises 1/11 of the side length of the monitor.

(2) The area of the frame alone is 42


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Normally I approach with easy options.

To Calculate the area of square, we need side of that square.
Since Diagonal of frame is given, we can calculate the side of monitor and hence the area of monitor.

In Option 2 - Area of Frame is given so can calculate the area of screen and then its Diagonal
Therefore A B C D E

In Option 1 - We can calculate the side of frame from given data.
and then we have given frame's dimension from which we can calculate the side of screen.

So A B C D E
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The front face of a square computer monitor consists of a square compu 02 May 2023, 05:27
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