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Which of the following equations is NOT equivalent

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boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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Which of the following equations is NOT equivalent

Post Tue May 03, 2016 2:46 pm
Which of the following equations is NOT equivalent to 10y^2 = (x+2)(x-2)?

A) 30y^2 = 3x^2 - 12

B) 20y^2 = (2x - 4)(x + 2)

C) 10y^2 + 4 = x^2

D) 5y^2 = x^2 - 2

E) y^2 = (x^2 - 4)/10

OA: D

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OptimusPrep Master | Next Rank: 500 Posts
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Post Tue May 03, 2016 7:27 pm
boomgoesthegmat wrote:
Which of the following equations is NOT equivalent to 10y^2 = (x+2)(x-2)?

A) 30y^2 = 3x^2 - 12
B) 20y^2 = (2x - 4)(x + 2)
C) 10y^2 + 4 = x^2
D) 5y^2 = x^2 - 2
E) y^2 = (x^2 - 4)/10

OA: D
Given: 10y^2 = (x+2)(x-2)
Or 10y^2 = x^2 - 4

We can solve it by assuming values of x and y or simply by rearranging the options.
Let us start rearranging the options that look easy first.

A) 30y^2 = 3x^2 - 12 => Cancelling out 3 from both sides, 10y^2 = x^2 - 4
C) 10y^2 + 4 = x^2 => On rearranging, 10y^2 = x^2 - 4
D) 5y^2 = x^2 - 2 => Multiplying by 2 on both sides, 10y^2 = 2x^2 - 4.
This is not equal to 10y^2 = x^2 - 4

We do not need to check for the other options.

Correct Option: D

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