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

Question

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 = \frac{(y^2 - 9)}{4}

EMPOWERgmatRichC · Answer

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:  D

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

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

Ralphcuisak · Answer

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.

EMPOWERgmatRichC · Answer

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

BrushMyQuant · Answer

Do we need to tag functions and custom characters in this? I think it is plain algebra with all standard characters (no custom characters)?

abhishekpasricha · Answer

We can always look for number plugging method as well because sometimes equations get difficult to be compared.

Here taking x =2 & y =5 satisfies the equation, plugging the same number in the list of options only D : 2x = y -3 does not satisfy the equation.

Hence D

CrackverbalGMAT · Answer

A quick look at the options and you see that Option D looks odd.

Squaring both sides, we have  (2x)^2 = (y + 3)^2 . Therefore  4x^2 = y^2 + 6x + 9  and this is not the same as the original expression.

All other options are just another form of the basic equation

Option A  :  4x^2 + 9 = y^2 . Therefore  4x^2 = y^2 - 9

Option B  :  4x^2 - y^2 = -9 . Therefore  4x^2 = y^2 - 9

Option C  :  4x^2 = (y + 3)(y - 3) . Therefore  4x^2 = y^2 - 9

Option E  :  x^2 = \frac{y^2 - 9}{4} . Therefore  4x^2 = y^2 - 9

Option D

Arun Kumar

Kinshook · Answer

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

(A)  4x^2+ 9 = y^2 
Equivalent
(B)  4x^2 - y^2 = -9 
Equivalent
(C)  4x^2= (y + 3)(y - 3) 
Equivalent
(D)  2x = y - 3 
Not equivalent
(E)  x^2 = \frac{(y^2 - 9)}{4} 
Equivalent

IMO D

sritamabanerjee · Answer

what is the level of this question?

Bunuel · Answer

You can check the difficulty level of a question along with the stats on it in the first post. For this question Difficulty = Sub-600 Level. The difficulty level of a question is calculated automatically based on the timer stats from the users which attempted the question.

bumpbot · Answer

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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 ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards