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The size of a flat-screen television is given as the length of the

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The size of a flat-screen television is given as the length of the  [#permalink]

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New post 26 Jul 2016, 09:59
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The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television?

A. 106.75
B. 213.5
C. 427
D. 729
E. 1,156

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Re: The size of a flat-screen television is given as the length of the  [#permalink]

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New post 26 Jul 2016, 10:11
34^2-27^2 = 427

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Re: The size of a flat-screen television is given as the length of the  [#permalink]

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New post 26 Jul 2016, 10:18
Diagonal of a square =√2*side of square
=> side =Diagonal/(√2)
Area of square =s*s
=(diagonal^2)/2

Difference of both tv's =(34^2-27^2)/2
=427
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Re: The size of a flat-screen television is given as the length of the  [#permalink]

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New post 26 Jul 2016, 10:48
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Bunuel wrote:
The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television?

A. 106.75
B. 213.5
C. 427
D. 729
E. 1,156



If we take a square with side length x and draw a diagonal, we get two isosceles right triangles.
If we focus on one such right triangle, we see that the legs have length x.

square 34-inch flat-screen television
The diagonal (hypotenuse) = 34
So, we can apply the Pythagorean Theorem to get x² + x² = 34²
Simplify: 2x² = 34²
Divide both sides by 2 to get: x² = 34²/2
Since the area of the square = x², we can see that the area of this square is 34²/2

square 27-inch flat-screen television
The diagonal (hypotenuse) = 27
So, we can apply the Pythagorean Theorem to get x² + x² = 27²
Simplify: 2x² = 27²
Divide both sides by 2 to get: x² = 27²/2
Since the area of the square = x², we can see that the area of this square is 27²/2

DIFFERENCE IN AREAS = 34²/2 - 27²/2

IMPORTANT: Before we perform any calculations, SCAN the answer choices.
Now notice that 34²/2 = (some EVEN integer)/2 = SOME INTEGER
Also, notice that 27²/2 = (some ODD integer)/2 = SOMETHING.5

So, 34²/2 - 27²/2 = SOME INTEGER - SOMETHING.5
= something.5
Perfect - only answer choice works!!

Answer:

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Re: The size of a flat-screen television is given as the length of the  [#permalink]

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New post 26 Jul 2016, 10:53
ShravyaAlladi wrote:
Diagonal of a square =√2*side of square
=> side =Diagonal/(√2)
Area of square =s*s
=(diagonal^2)/2

Difference of both tv's =(34^2-27^2)/2
=427


Missed to divide
427/2 =213.5


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Re: The size of a flat-screen television is given as the length of the  [#permalink]

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New post 26 Jul 2016, 10:57
GMATPrepNow wrote:
Bunuel wrote:
The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television?

A. 106.75
B. 213.5
C. 427
D. 729
E. 1,156



If we take a square with side length x and draw a diagonal, we get two isosceles right triangles.
If we focus on one such right triangle, we see that the legs have length x.

square 34-inch flat-screen television
The diagonal (hypotenuse) = 34
So, we can apply the Pythagorean Theorem to get x² + x² = 34²
Simplify: 2x² = 34²
Divide both sides by 2 to get: x² = 34²/2
Since the area of the square = x², we can see that the area of this square is 34²/2

square 27-inch flat-screen television
The diagonal (hypotenuse) = 27
So, we can apply the Pythagorean Theorem to get x² + x² = 27²
Simplify: 2x² = 27²
Divide both sides by 2 to get: x² = 27²/2
Since the area of the square = x², we can see that the area of this square is 27²/2

DIFFERENCE IN AREAS = 34²/2 - 27²/2

IMPORTANT: Before we perform any calculations, SCAN the answer choices.
Now notice that 34²/2 = (some EVEN integer)/2 = SOME INTEGER
Also, notice that 27²/2 = (some ODD integer)/2 = SOMETHING.5

So, 34²/2 - 27²/2 = SOME INTEGER - SOMETHING.5
= something.5
Perfect - only answer choice works!!

Answer:

RELATED VIDEOS:






213.5 is giving only the half difference on the side of 2 squares




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The size of a flat-screen television is given as the length of the  [#permalink]

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New post 26 Jul 2016, 14:12
\(d_1 = 34\\
d_2 = 27\)

From Pythagoras: \(\sqrt{a^2 + b^2} = d\).
For Pythagoras on a square, \(a=b \implies \sqrt{2a^2} = d\)
Area of a square: \(a^2\), in this case: \(a^2 = \frac{d^2}{2}\)
Subtract the two areas to obtain the formula: \(\frac{d_1^{\,2}}{2} - \frac{d_2^{\,2}}{2}\)
\(= \frac{1}{2}(d_1^{\,2}-d_2^{\,2})\)
\(= \frac{1}{2}(1156 - 729) = \frac{427}{2} = 213.5\)


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Re: The size of a flat-screen television is given as the length of the  [#permalink]

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New post 26 Jul 2016, 18:57
Bunuel wrote:
The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television?

A. 106.75
B. 213.5
C. 427
D. 729
E. 1,156


Area of square= diagonal^2/2

How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television?
34^2/2- 27^2/2

units digit of 34^2= 6
Units digit of 27^2= 9

6-9 will generate 7 as the units digit and 7/2 will generate .5 at the end. Only option B has this form.

B is the answer
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Re: The size of a flat-screen television is given as the length of the  [#permalink]

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New post 30 Jul 2016, 07:31
Bunuel wrote:
The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television?

A. 106.75
B. 213.5
C. 427
D. 729
E. 1,156


Diagonal is x√2

For bigger 34 inch TV
Diagonal x√2=34
Side x=34/√2
Area x^2=\(34^2\)/2

For Smaller 27 inch TV
Diagonal x√2=27
Side x=27/√2
Area x^2=\(27^2\)/2

Difference = (1156-729)/2 = 427/2 = 213.1

Answer is B
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Re: The size of a flat-screen television is given as the length of the  [#permalink]

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