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Which of the following equations is NOT equivalent

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Which of the following equations is NOT equivalent

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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

The OA is D.

Experts, what is the best approach to solve this PS question? I'd really appreciate an answer. Thanks.

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GMAT/MBA Expert

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Quote:
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

The OA is D.

Experts, what is the best approach to solve this PS question? I'd really appreciate an answer. Thanks.
Hi Vincen,
Let's take a look at your question.

To find out which of the given options is not equivalent to 10y^2=(x+2)(x-2), we will check each option one by one.
The equation $$10y^2=\left(x+2\right)\left(x-2\right)$$ can also be written as,
$$10y^2=x^2-4$$
So the equivalent expressions can be equal to either of the represetation.

Let's start by Option A.
$$30y^2=3x^2-12$$
$$3\left(10\right)y^2=3\left(x^2-4\right)$$
$$10y^2=x^2-4$$
Which is equivalent to the given expression.

Option B.
$$20y^2=\left(2x-4\right)\left(x+2\right)$$
$$2\left(10\right)y^2=2\left(x-2\right)\left(x+2\right)$$
$$10y^2=\left(x-2\right)\left(x+2\right)$$
Which is equivalent to the given expression.

Option C.
$$10y^2+4=x^2$$
$$10y^2=x^2-4$$
Which is equivalent to the given expression.

Option D.
$$5y^2=x^2-2$$
This expression is not equivalent to the given expression.
Even if we try multiplying the equation by 2, so that we can make 10y^2 at the left side, we will end up with,
$$10y^2=2x^2-4$$
Which is different from the equation given.

Therefore, Option D is correct.

Hope this helps.
I am available if you'd like any follow up.

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GMAT/MBA Expert

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Vincen 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
Let x=2.
Plugging x=2 into 10y² = (x+2)(x-2), we get:
10y² = (2+2)(2-2)
10y² = (4)(0)
10y² = 0
y² = 0.

Since x=2 and y²=0 are a valid solution for 10y² = (x+2)(x-2), they must also be a valid solution for any equation that is the equivalent of 10y² = (x+2)(x-2).
Strategy:
Plug x=2 and y²=0 into the answer choices to see which answer choice does NOT work.
Note:
When the question stem includes the phrase which of the following, the correct answer is likely to be D or E.

E. y²= (x²-4)/10
0 = (2²-4)/10
0 = 0.
This works.
Eliminate E.

D. 5y² = x² - 2
5(0) = 2² - 2
0 = 4 - 2
0 = 2.
Doesn't work.

The correct answer is D.

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