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

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Math Expert
Joined: 02 Sep 2009
Posts: 58402
The size of a flat-screen television is given as the length of the  [#permalink]

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26 Jul 2016, 09:59
1
5
00:00

Difficulty:

65% (hard)

Question Stats:

63% (02:28) correct 37% (02:42) wrong based on 94 sessions

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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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Posts: 315
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Re: The size of a flat-screen television is given as the length of the  [#permalink]

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

C

Intern
Joined: 29 Jun 2016
Posts: 41
Re: The size of a flat-screen television is given as the length of the  [#permalink]

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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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Joined: 12 Sep 2015
Posts: 4007
Re: The size of a flat-screen television is given as the length of the  [#permalink]

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26 Jul 2016, 10:48
Top Contributor
3
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!!

RELATED VIDEOS:

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

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26 Jul 2016, 10:53
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

Senior Manager
Joined: 11 Nov 2014
Posts: 315
Location: India
WE: Project Management (Telecommunications)
Re: The size of a flat-screen television is given as the length of the  [#permalink]

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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!!

RELATED VIDEOS:

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

Manager
Joined: 07 Jul 2016
Posts: 74
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The size of a flat-screen television is given as the length of the  [#permalink]

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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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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.

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

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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

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

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24 Aug 2018, 10:53
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Re: The size of a flat-screen television is given as the length of the   [#permalink] 24 Aug 2018, 10:53
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