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# Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?

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Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  [#permalink]

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14 Jan 2015, 23:05
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Which of the following equations is NOT equivalent to $$4x^2$$ = $$y^2$$- 9 ?

(A) $$4x^2$$+ 9 = $$y^2$$
(B) $$4x^2$$ - $$y^2$$ = -9
(C) $$4x^2$$= (y + 3)(y - 3)
(D) 2x = y - 3
(E) $$x^2$$ = ($$y^2$$-9)/4

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Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  [#permalink]

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14 Jan 2015, 23:29
Hi abhisheknandy08,

This question is based on the various ways that you're mathematically "allowed" to manipulate an equation. We're asked to find the answer that is NOT the equivalent of the equation in the prompt.

We're given 4X^2 = Y^2 - 9

I'm going to work through the answers, starting with A....

A: If we ADD 9 to both sides, we'd have...
4X^2 + 9 = Y^2
This IS EQUIVALENT.

B: If we SUBTRACT Y^2 from both sides, we'd have....
4X^2 - Y^2 = -9
This IS EQUIVALENT.

C: If we FACTORED the "right side" of the equation, we'd have...
4X^2 = (Y+3)(Y-3)
This IS EQUIVALENT.

D: There's no acceptable math rule we can use to get to this answer.
This is NOT equivalent.

E: If we DIVIDE both sides by 4, we'd have....
X^2 = (Y^2 - 9)/4
This IS EQUIVALENT.

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Math Expert Joined: 02 Sep 2009 Posts: 47977 Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ? [#permalink] ### Show Tags 15 Jan 2015, 01:05 abhisheknandy08 wrote: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ? (A) 4x^2 + 9 = y^2 (B) 4x^2 - y^2 = -9 (C) 4x^2= (y + 3)(y - 3) (D) 2x = y - 3 (E)x^2 = (y^2-9)/4 Similar questions to practice: which-of-the-following-is-not-equivalent-to-49a-2-9b-188518.html which-of-the-following-equations-is-not-equivalent-to-10y-138730.html _________________ Current Student Status: The Final Countdown Joined: 07 Mar 2013 Posts: 287 Concentration: Technology, General Management GMAT 1: 710 Q47 V41 GPA: 3.84 WE: Information Technology (Computer Software) Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ? [#permalink] ### Show Tags 15 Jan 2015, 01:16 Could you please elaborate on D..Why is it not possible and what is possible in such a scenario(when an expression has both squares and roots and we want to eliminate them)?I'm having trouble with this concept. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12189 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ? [#permalink] ### Show Tags 15 Jan 2015, 20:26 Hi Ralphcuisak, Here's why you can't re-write/reduce/simplify the prompt to what's listed in Answer D: We're given..... 4X^2 = Y^2 - 9 The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt. Looking at Answer D, we have.... 2X = Y - 3 While you COULD take the square root of both sides of the original equation, it's important to note that the square root of Y^2 - 9 is NOT (Y-3). Y^2 - 9 can be factored into (Y-3)(Y+3), but neither of these parentheses is the square root of Y^2 - 9. You can see the proof when you square either of the two parentheses: (Y-3)^2 = Y^2 - 6X + 9 (Y+3)^2 = Y^2 + 6x + 9 Thus, D is NOT equivalent to the prompt. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  [#permalink]

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17 Jul 2015, 23:59
1
Do we need to tag functions and custom characters in this? I think it is plain algebra with all standard characters (no custom characters)?
abhisheknandy08 wrote:
Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?

(A) 4x^2 + 9 = y^2
(B) 4x^2 - y^2 = -9
(C) 4x^2= (y + 3)(y - 3)
(D) 2x = y - 3
(E)x^2 = (y^2-9)/4

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Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  [#permalink]

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16 Dec 2017, 03:45
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