Last Updated on May 4, 2023
GMAT OFFICIAL GUIDE PS
Solution:
To solve this question, we start by FOILing the right hand side of the given equation.
10y^2 = (x+2)(x-2)
10y^2 = x^2 – 4
We will manipulate each of the answer choices to see if it equals 10y^2 = x^2 – 4. Let’s start with A.
A) 30y^2 =3x^2 – 12
If we divide this entire equation by 3 we are left with:
10y^2 = x^2 – 4
Answer choice A is not correct.
B) 20y^2 = (2x-4)(x+2)
FOILing (2x-4)(x+2) we get:
20y^2 = 2x^2 – 8
If we divide this entire equation by 2 we obtain:
10y^2 = x^2 – 4
Answer choice B is not correct.
C) 10y^2 + 4 = x^2
If we subtract 4 from the both sides of the equation, we obtain:
10y^2 = x^2 – 4
Answer choice C is not correct.
D) 5y^2 = x^2 – 2
We should notice that no matter how we try to manipulate 5y^2 = x^2 – 2, it will never be equal to 10y^2 = x^2 – 4. For example, if we multiply both sides of 5y^2 = x^2 – 2 by 2, we will have 10y^2 = 2x^2 – 4. However, that is not the same as 10y^2 = x^2 – 4.
Answer D is correct.
To be certain, we should also test answer E.
E) y^2 = (x^2 – 4)/10
If we multiply the entire equation by 10 we obtain:
10y^2 = x^2 – 4
Answer choice E is not correct.
Answer: D
