Which of the Following Equation is NOT Equivalent to 25x^2 = y^2 - 4? GMAT Problem Solving

Question: Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?

1. 25x^2 + 4 = y^2
2. 75x^2 = 3y^2 - 12
3. 25x^2 = (y + 2)(y - 2)
4. 5x = y - 2
5. x^2 = (y^2 - 4)/25

‘Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?’ - is a topic of the GMAT Quantitative reasoning section. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have good knowledge of qualitative skills. The GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:
Given in the question an equation 25\(x^2\) = \(y^2\)- 4
It is asked to find out which of the given five equations is not equivalent to this equation.
We have to check each and every option one by one.
In option 1,
25\(x^2\) + 4 = \(y^2\)
Taking four to right hand side we get,
25\(x^2\) = \(y^2\)- 4
This is the same as the given equation hence this cannot be the answer.
In option 2 it is given that 75\(x^2\) = 3\(y^2\) - 12
Dividing each side by 3 we get.
(75/3)\(x^2\) = (3/3)\(y^2\) - 12/3
25\(x^2\) = \(y^2\)- 4
This is the same as the given equation hence this cannot be the answer.
In option 3 it is given that,
25\(x^2\) = (y+2)(y-2)
25\(x^2\) = \(y^2\)- 2y + 2y - 4
25\(x^2\) = \(y^2\)- 4
This is the same as the given equation hence this cannot be the answer.
In option 4 it is given that,
5x = y -2
This is a linear equation and given to us is a quadratic equation, so they cannot be equivalent
This is the correct answer.
In option 5,
\(x^2\)= (\(y^2\)-4)/25
taking 25 to left hand side,
25\(x^2\) = \(y^2\)- 4
This is the same as the given equation hence this cannot be the answer.
Therefore the correct answer is option D.

Correct Answer: D

Approach Solution 2:
Given in the question an equation 25\(x^2\) = \(y^2\)- 4
It is asked to find out which of the given five equations is not equivalent to this equation.
We have to check each and every option one by one.
|Option A- 25\(x^2\) + 4 = \(y^2\)(take 4 from LHS to RHS)
Option B - 75\(x^2\) =3\(y^2\) -12 ( divide both sides by 4)
Option C - 25\(x^2\) = (y+2)(y-2) (multiply both terms in RHS)
Option D - 5x = y -2 (not possible in any way)
Option E - \(x^2\)= (\(y^2\)-4)/25 (multiply 25 to both sides)
Option D is the only option that is not equivalent to the given equation.

Correct Answer: D

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