Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?

Answer = E

Original Equation

\(49a^2 = 9b^2 - 4\)

Option A, B, C, D are same as the original equation.... adjusting terms of LHS/RHS, multiply by 2 etc...

Option E

Square root the original equation

\(7a = \sqrt{9b^2 - 4} = \sqrt{(3b+2)(3b-2)}\) .... This only far the equation can go

We just need to adjust equation as per the options and verify.

49a^2 = 9b^2 - 4 => 49a^2 + 4 = 9b^2 ----> Option a

Multiply by 2,
98a^2 = 18b^2 - 8 ----> Option b

49a^2 = 9b^2 - 4 => 49a^2 = (3b + 2)(3b - 2) ---> option c

a^2 = 9b^2 - 4 / 49 => a^2 = 9b^2 - 4 /7^2 ---- > option d

Take square root on both the sides
7a = \(\sqrt{9b^2 - 4}\) = \(\sqrt{(3b+2)(3b-2)}\) => This is not equal to 7a = 3b - 2

Hence answer is E.

Official Solution:

Which of the following is NOT equivalent to \(49a^2 = 9b^2 - 4\)?

A. \(49a^2 + 4 = 9b^2\)
B. \(98a^2 = 18b^2 - 8\)
C. \(49a^2 = (3b - 2)(3b + 2)\)
D. \(a^2 = \frac{9b^2 - 4}{7^2}\)
E. \(7a = 3b - 2\)


Four of the answer choices are equivalent to \(49a^2 = 9b^2 - 4\), and one is not. Equations are said to be equivalent when the equations have the same solution.

In this case, equivalent equations will have the same value for \(a\) and \(b\) as in the original equation. Let's compare our equation to each choice.

Choice A: \(49a^2 + 4 = 9b^2\) is the same as the original equation if 4 is added to both sides. Eliminate A.

Choice B: \(98a^2 = 18b^2 - 8\) is the same as the original equation if both sides are multiplied by 2. Eliminate B.

Choice C: \(49a^2 = (3b - 2)(3b + 2)\) correctly factors the original equation. Eliminate C.

Choice D: \(a^2 = \frac{9b^2 - 4}{7^2}\) is the same as the original equation if both sides are divided by \(7^2\) or \(49\). Eliminate D.

Choice E: \(7a = 3b - 2\) incorrectly calculates the square root of \(9b^{2} - 4\). The square root of the left side of the equation is correctly calculated. However, the square root of \(9b^{2} - 4\) isn't \(3b - 2\). We can verify this by squaring \(3b - 2\). If we do, we get \(9b^{2} - 12b + 4\), which is not equivalent to \(9b^{2} - 4\).

Choice E, which is not equivalent, is thus correct.


Answer: E.

Similar question from OG13: which-of-the-following-equations-is-not-equivalent-to-10y-138730.html

Let’s analyze each answer choice.

A. 49a^2 + 4 = 9b^2

If we subtract 4 from both sides of the equation, we have 49a^2 = 9b^2 - 4. This is equivalent.

B. 98a^2 = 18b^2 - 8

If we divide both sides of the equation by 2, we have 49a^2 = 9b^2 - 4. This is equivalent.

C. 49a^2 = (3b - 2)(3b + 2)

If we expand the right-hand side of the equation, we have 49a^2 = 9b^2 - 4. This is equivalent.

D. a^2 = (9b^2 - 4)/7^2

If we divide both sides of the equation by 7^2 = 49, we have 49a^2 = 9b^2 - 4. This is equivalent.

Thus, the correct answer must be E. However, let’s analyze it anyway.

E. 7a = 3b - 2

If we square both sides of the equation, we have (7a)^2 = (3b - 2)^2, or 49a^2 = 9b^2 - 12b + 4, which is not the same is 49a^2 = 9b^2 - 4.

Answer: E

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.