Difference of areas of 2 TVs

Question

The size of a television screen is given as the length of the screen’s diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen?

(A) 2
(B) 4
(C)16
(D)38
(E)40

OA is E.

Thanks,
Bharat.

theCodeToGMAT · Answer

Size = Diagnol = side * sqrt(2) Area of 21 inch - Area of 19 Inch (21/sqrt(2))^2 - (19/sqrt(2))^2 1/2 (21+19)(21-19) = 1/2 * 40 * 2 = 40 Answer [spoiler]{E}[/spoiler]

ganeshrkamath · Answer

pareekbharat86 wrote:The size of a television screen is given as the length of the screen’s diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen?

(A) 2
(B) 4
(C)16
(D)38
(E)40

OA is E.

The diagonal of a square with sides of length a = a sqrt(2)
Area of the square = a^2 = (diagonal^2)/2

Area of 21-inch screen = 1/2 * 21^2
Area of 19-inch screen = 1/2 * 19^2

Difference = 1/2 * (21^2 - 19^2)
= 1/2 * (21 + 19) * (21 - 19)
= 1/2 * (40) * (2)
= 40 sq. inches

Choose E

Cheers

Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494

Rich.C@EMPOWERgmat.com · Answer

Hi pareekbharat86,

Rahul has properly explained the math behind this question. Here's the pattern that you need to know:

GMAT geometry questions emphasize certain formulas and relationships. Here, it's worth noting that EVERY square can be broken down into 2 45/45/90 triangles.

45/45/90 triangles have a relationship among their sides: X/X/X(root2)

Be on the lookout for this rule, as it's likely to be something that you're tested on during your Official GMAT.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

GMATGuruNY · Answer

pareekbharat86 wrote:The size of a television screen is given as the length of the screen’s diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen?

(A) 2
(B) 4
(C)16
(D)38
(E)40

OA is E.

The diagonal of a square with sides of length a = a sqrt(2)
Area of the square = a^2 = (diagonal^2)/2

Area of 21-inch screen = 1/2 * 21^2
Area of 19-inch screen = 1/2 * 19^2

Difference = 1/2 * (21^2 - 19^2)
= 1/2 * (21 + 19) * (21 - 19)
= 1/2 * (40) * (2)
= 40 sq. inches

Choose E

Cheers

Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494

pareekbharat86 · Answer

Thanks all of you. My brain's got so fried with so much practicing that I kept getting 20 as the answer. I was using 1/2*base*height formula for a square!!! My bad.

rairavig · Answer

in above solutions it is clear the the difference between both areas can be calculated as:

Difference = 1/2 * (21^2 - 19^2) ..... (A)

here i wana advise a general way to calculate the difference between to squares.
i.e
(n+1)^2 - n^2 = 2n+1
(n+2)^2 - n^2 = 2(2n+2)
(n+3)^2 - n^2 = 3(2n+3)
.....

so here we may consider 19 as "n" so "n+2" is 21.
and difference in area is
Difference = 1/2 * (21^2 - 19^2):
Difference = 1/2 * (19+2)^2 - 19^2 = 1/2 * 2(2*19+2)= 40

this is more efficient way to find difference between big squares.
hope you like.

vipulgoyal · Answer

awesome, did you drive it with this PS ??

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