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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 13 Mar 2013 Posts: 165 Location: United States Concentration: Leadership, Technology GPA: 3.5 WE: Engineering (Telecommunications) Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ? [#permalink] ### Show Tags 14 Jan 2015, 22:05 4 00:00 Difficulty: 5% (low) Question Stats: 93% (00:52) correct 7% (01:06) wrong based on 234 sessions ### HideShow timer Statistics 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 Edit: Formatting _________________ Regards , EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12856 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 14 Jan 2015, 22:29 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. Final Answer: 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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15 Jan 2015, 00:05
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

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

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15 Jan 2015, 00:16
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.
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Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  [#permalink]

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15 Jan 2015, 19:26
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.

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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, 22:59
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, 02:45
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Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ? &nbs [#permalink] 16 Dec 2017, 02:45
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