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# A computer manufacturer claims that a perfectly square computer

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Retired Moderator
Joined: 18 Sep 2014
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A computer manufacturer claims that a perfectly square computer  [#permalink]

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28 Feb 2016, 01:03
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Difficulty:

65% (hard)

Question Stats:

66% (02:53) correct 34% (03:14) wrong based on 131 sessions

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A computer manufacturer claims that a perfectly square computer monitor has a diagonal size of 20 inches. However, part of the monitor is made up of a plastic frame surrounding the actual screen. The area of the screen is three times the size of that of the surrounding frame. What is the diagonal of the screen?

A. $$\sqrt{125}$$
B. $$\frac{20}{3}$$
C. $$\frac{20}{\sqrt{3}}$$
D. $$\sqrt{150}$$
E. $$\sqrt{300}$$

Caution: Don't go for finer details such as Frame thickness as it will be a waste of time and effort.
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Re: A computer manufacturer claims that a perfectly square computer  [#permalink]

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28 Feb 2016, 22:56
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6
Nevernevergiveup wrote:
A computer manufacturer claims that a perfectly square computer monitor has a diagonal size of 20 inches. However, part of the monitor is made up of a plastic frame surrounding the actual screen. The area of the screen is three times the size of that of the surrounding frame. What is the diagonal of the screen?

A. $$\sqrt{125}$$
B. $$\frac{20}{3}$$
C. $$\frac{20}{\sqrt{3}}$$
D. $$\sqrt{150}$$
E. $$\sqrt{300}$$

Caution: Don't go for finer details such as Frame thickness as it will be a waste of time and effort.

Diagonal of the monitor is 20 inches so side of the square monitor is $$20/\sqrt{2}$$. So area of the complete monitor is $$Side^2 = 400/2 = 200$$ square inches.

Area of screen is 3 times area of frame. Total area of both together is 200. So area of screen is 150 and area of frame is 50.

Side of the screen $$= \sqrt{150}$$

Diagonal of the screen = $$Side*\sqrt{2} = \sqrt{150}*\sqrt{2} = \sqrt{300}$$

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Re: A computer manufacturer claims that a perfectly square computer  [#permalink]

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28 Feb 2016, 01:19
Nevernevergiveup wrote:
A computer manufacturer claims that a perfectly square computer monitor has a diagonal size of 20 inches. However, part of the monitor is made up of a plastic frame surrounding the actual screen. The area of the screen is three times the size of that of the surrounding frame. What is the diagonal of the screen?

A. 125
B. 203
C. 203
D. 150
E. 300

Caution: Don't go for finer details such as Frame thickness as it will be a waste of time and effort.

Both option B and C are same.

Here is my explanation.
Diagonal of a Square 20 inches.
A diagonal will bisect a Square into an isosceles triangle. Sides of the Isoc. triangle will be in the ratio 1:1:\sqrt{2}

From this we can conclude that the sides of the complete square including the frame is 20. Hence the area of the complete square is 400 [A^2 = 20 * 20 = 400]_

Its given the screen area is 3times that of the frame. hence Area of screen:Area of frame = 3:1
4X = 400
X = 300sq.m is the area of the Screen excluding frame.

Diagonal is \sqrt{2} times the side of the square excluding frame. Which is \sqrt{600}

Am i missing anything here??
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Re: A computer manufacturer claims that a perfectly square computer  [#permalink]

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28 Feb 2016, 01:26
sowragu wrote:
Both option B and C are same.
Am i missing anything here??

Corrected the options.
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A computer manufacturer claims that a perfectly square computer  [#permalink]

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09 Sep 2016, 07:28
i think technically, the question is wrongly written...when someone says that diagonal of the monitor is X, it means the diagonal of the screen. check online for all major brands by what is meant when diagonal size is given.
i understood the question wrong just because of this shift in meaning.
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Re: A computer manufacturer claims that a perfectly square computer  [#permalink]

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20 Nov 2016, 11:15
I redone the question after few months...still think the question is written incorrectly.
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A computer manufacturer claims that a perfectly square computer  [#permalink]

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17 Jan 2018, 04:58
I am confused regarding the wordings here. Could some one explain how we can use the relation stated here "area of screen is three times the size of the frame. Does it mean area of the screen is thrice than the area of frame. Confused with the word " Size". VeritasPrepKarishma
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Re: A computer manufacturer claims that a perfectly square computer  [#permalink]

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17 Jan 2018, 05:12
rajatbanik wrote:
I am confused regarding the wordings here. Could some one explain how we can use the relation stated here "area of screen is three times the size of the frame. Does it mean area of the screen is thrice than the area of frame. Confused with the word " Size". VeritasPrepKarishma

Yes, it means {the area of the screen } = 3*{the area of the frame}.
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Re: A computer manufacturer claims that a perfectly square computer  [#permalink]

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26 Feb 2018, 11:16
1
Nevernevergiveup wrote:
A computer manufacturer claims that a perfectly square computer monitor has a diagonal size of 20 inches. However, part of the monitor is made up of a plastic frame surrounding the actual screen. The area of the screen is three times the size of that of the surrounding frame. What is the diagonal of the screen?

A. $$\sqrt{125}$$
B. $$\frac{20}{3}$$
C. $$\frac{20}{\sqrt{3}}$$
D. $$\sqrt{150}$$
E. $$\sqrt{300}$$

Since the diagonal = side√2, we have:

20 = side√2

20/√2 = side

Multiplying by √2/√2, we have:

10√2 = side

If we let each side of the monitor, not counting the frame = n, then we can create the following equation:

n^2 = 3[(10√2)^2 - n^2]

n^2 = 3[200 - n^2]

n^2 = 600 - 3n^2

4n^2 = 600

n^2 = 150

n = √150

So, the diagonal of the screen is √150 x √2 = √300.

Alternate Solution:

Since the diagonal = side√2, a side of the monitor is 20/√2 = 10√2. Thus, the area of the monitor, including the screen and the surrounding frame, is (10√2)^2 = 200.

If we let A denote the area of the surrounding frame, the area of the screen is 3A and thus, the total area of the monitor is 3A + A = 4A. Since 4A = 200, we find that A = 50 and the area of the screen is 3A = 150. Then, a side of the screen is √150 = 5√6. Finally, the diagonal of the screen is (5√6) x √2 = 5√12 = √300.

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Re: A computer manufacturer claims that a perfectly square computer  [#permalink]

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07 Jul 2019, 07:15
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Re: A computer manufacturer claims that a perfectly square computer   [#permalink] 07 Jul 2019, 07:15
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