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S95-28

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S95-28  [#permalink]

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New post 16 Sep 2014, 00:50
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

93% (00:24) correct 7% (00:46) wrong based on 27 sessions

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

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Re S95-28  [#permalink]

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New post 16 Sep 2014, 00:50
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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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: S95-28  [#permalink]

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New post 08 Dec 2017, 13:41
What is the square root of 9b^2 − 4, anyway?
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Re: S95-28 &nbs [#permalink] 08 Dec 2017, 13:41
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