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Which of the following equations is NOT equivalent

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by OptimusPrep » 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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by [email protected] » Sun Mar 11, 2018 11:27 am
Hi All,

We're asked which of the following equations is NOT equivalent to 10y^2 = (x+2)(x-2). This question ultimately comes down to 'rewriting' the given equation, so a little bit of math work is required.

To start, we can rewrite 10y^2 = (x+2)(x-2) as....
10y^2 = x^2 - 4

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

If we multiply BOTH sides of the given equation by 3, then we will end up with Answer A.

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

If we multiply BOTH sides of the given equation by 2, then we'll end up with...
20y^2 = 2x^2 - 8
We can then factor the 'right side' into:
2x^2 - 8 = (x+2)(2x-4)....
Thus, we will end up with Answer B.

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

If we add 4 to both sides of the equation, then we'll end up with Answer C.

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

If we divide BOTH sides of the given equation by 10, then we'll end up with Answer E.

There's only one answer that is NOT mathematically equivalent...

Final Answer: D

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by Scott@TargetTestPrep » Tue Mar 13, 2018 4:22 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
Simplifying the stem we have:

10y^2 = x^2 - 4

Let's analyze each answer choice:

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

Dividing by 3 we have:

10y^2 = x^2 - 4

Choice A is equivalent.

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

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

20y^2 = 2x^2 - 8

10y^2 = x^2 - 4

Choice B is equivalent.

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

10y^2 + 4 = x^2

10y^2 = x^2 - 4

Choice C is equivalent.

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

Multiplying by 2 we have:

10y^2 = 2x^2 - 4

Choice D is NOT equivalent.

Answer: D
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