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The size of a flat-screen television is given as the length of the
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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?
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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!!
Re: The size of a flat-screen television is given as the length of the
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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!!
The size of a flat-screen television is given as the length of the
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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: \(\frac{d_1^{\,2}}{2} - \frac{d_2^{\,2}}{2}\) \(= \frac{1}{2}(d_1^{\,2}-d_2^{\,2})\) \(= \frac{1}{2}(1156 - 729) = \frac{427}{2} = 213.5\)
Re: The size of a flat-screen television is given as the length of the
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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.
B is the answer
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Re: The size of a flat-screen television is given as the length of the
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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
Answer is B
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24 Aug 2018, 10:53
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