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

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

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New post 13 Nov 2014, 08:47
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Tough and Tricky questions: Algebra.



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. \(7a = 3b - 2\)

Kudos for a correct solution.

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Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

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New post 13 Nov 2014, 09:10
I chose to put everything on one side of the equal sign.

49a^2 - 9b^2 - 4 = 0

Answer A: move everything to one side to get 49^2 - 9b^2 - 4 = 0, not equivalent

Answer A!
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Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

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New post 13 Nov 2014, 09:13
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Bunuel wrote:

Tough and Tricky questions: Algebra.



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. \(7a = 3b - 2\)

Kudos for a correct solution.


I tried to look for the common traps people face when they simplify equations. My attention went to choice E.

The reason is because it tries to simplify by square root-ing the equation, but the square root of \(9b^2 - 4\) does not equal \(3b - 2\). It factors to \((3b+2)(3b-2)\).

Therefore I know it is not equivalent to the equation in the question stem.

If I really wanted to validate that the other choices are in fact wrong, most of them require very simple algebraic operations to prove which can be done without pen and paper even.

A) Just add +4 to both sides.
B) Multiply both sides by 2.
C) Factor the right side of the equation. (This is what answer choice E tries to trap with.)
D) Divide both sides by 49,
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Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

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New post 13 Nov 2014, 20:13
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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
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Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

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New post 14 Nov 2014, 05:20
1
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.
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Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

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New post 14 Nov 2014, 08:25
Bunuel wrote:

Tough and Tricky questions: Algebra.



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. \(7a = 3b - 2\)

Kudos for a correct solution.


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.
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Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

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New post 14 Nov 2014, 08:26
Bunuel wrote:

Tough and Tricky questions: Algebra.



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. \(7a = 3b - 2\)

Kudos for a correct solution.


Similar question from OG13: which-of-the-following-equations-is-not-equivalent-to-10y-138730.html
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4?  [#permalink]

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New post 29 Sep 2017, 09:21
Bunuel wrote:

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. \(7a = 3b - 2\)


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
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Re: Which of the following is NOT equivalent to 49a^2 = 9b^2 - 4? &nbs [#permalink] 29 Sep 2017, 09:21
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