Which of the following Equation is NOT equivalent to 25x^2=y^2-4?

Question

Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?

A) 25x^2 + 4 = y^2
B) 75x^2 = 3y^2 - 12
C) 25x^2 = (y + 2)(y - 2)
D) 5x = y - 2
E) x^2 = (y^2 - 4)/25

This Question i have taken from Jamboree red book, and while searching over the internet i got to know it's a very old OG question,as per the answer sheet D is the answer, could someone please tell me why?
Thanks In Advance.

GMATinsight · Accepted Answer

Let's Solve the given equation first

25x^2 = y^2 - 4
i.e. (5x)^2 - y^2 = -4
i.e. y^2 - (5x)^2 = 4

Let's Check the Options:

A) 25x^2 + 4 = y^2
This equation can be re-written as 
25x^2 = y^2 - 4   which is same as Equation given in question hence Option ELIMINATED

B) 75x^2 = 3y^2 - 12
Divide the equation by 3 on both sides, we get 
25x^2 = y^2 - 4   which is same as Equation given in question hence Option ELIMINATED

C) 25x^2 = (y + 2)(y - 2)
This equation can be re-written as 
25x^2 = y^2 -2y+2y - 4
i.e. 25x^2 = y^2 - 4   which is same as Equation given in question hence Option ELIMINATED

D) 5x = y - 2   Hence, The correct Answer Option

E) x^2 = (y^2 - 4)/25
Multiply the equation on both sides by 25
i.e. 25x^2 = y^2 - 4   which is same as Equation given in question hence Option ELIMINATED

I hope it helps!

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 which-of-the-following-equations-is-not-equivalent-to-4x-2-y-191665.html Hope it helps.

jaspreets · Answer

I wonder why the answer is D?

TimeTraveller · Answer

Option (A): It's a simple realignment of the original equation, so it's the same.

Option (B): Multiplied by 3, same.

Option (C): LHS is the same, RHS is expressed in a different form, (a^2 - b^2) = (a+b) (a-b). Same.

Option (D): y^2 - 4 is not equal to y-2, from Option (C) we can see that (y^2 - 4) = (y+2) (y-2). So this is not the same as the original equation.

Option (E): Multiplying both sides by 25 we get the original equation, so it's also the same.

So, we arrived at the solution in 2 ways.

mejia401 · Answer

Writing down how each answer choice was different, I came up with:
 A. Add four to both sides 
 B. Multiplied by three to both sides 
 C. RHS is the difference of squares, nothing changed 
 D. Only six operations can be done to expressions: add, subtract, multiply, divide, take root, or raise to a power. None of them will bring us to this answer choice. 
 E. Divided by 25 both sides

D.

EMPOWERgmatRichC · Answer

Hi jaspreets,

With this question, you can either...
1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers
2) Take each answer choice and see if you can manipulate it to make it into the original equation.

With Answer D, we have...

5X = Y - 2

If we square both sides, we end up with....

(5X)^2 = (Y-2)^2
(5X)(5X) = (Y-2)(Y-2)

25X^2 = Y^2 - 4Y + 4

This is NOT a match for the original equation, so it's the answer that is NOT equivalent.

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

BrentGMATPrepNow · Answer

Two small points to note: 1) This is actually an official question from the 10th edition of the Official Guide 2) This question requires us to check/test each answer choice . In these situations, always check the answer choices from E to A , because the correct answer is typically closer to the bottom than to the top. For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions Cheers, Brent

ScottTargetTestPrep · Answer

Let’s check each answer choice:

Choice A. If we move -4 to the left side of the given equation, we will obtain 25x^2 + 4 = y^2. Choice A is equivalent.

Choice B. If we multiply each side of the given equation by 3, we will obtain 75x^2 = 3y^2 - 12. Choice B is equivalent.

Choice C. If we factor the right hand side of the equation, we obtain 25x^2 = (y + 2)(y - 2). Choice C is equivalent.

Choice D. Since there is no way to manipulate 5x = y - 2 to equal 25^2 = y^2 - 4, we see that answer choice D is correct.

Choice E. If we divide each side of the given equation by 25, we obtain x^2 = (y^2 - 4)/25. Choice E is equivalent.

Answer: D

Kinshook · Answer

hich of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?

A) 25x^2 + 4 = y^2
25x^2 = y^2 - 4
Equivalent
B) 75x^2 = 3y^2 - 12
3 * Equation ; Equivalent
C) 25x^2 = (y + 2)(y - 2)
25x^2 = y^2 - 4
Equivalent
D) 5x = y - 2
Not Equivalent
E) x^2 = (y^2 - 4)/25
25x^2 = y^2 - 4
Equivalent

IMO D

Abhishek009 · Answer

25x^2 = y^2 - 4

Or,  25x^2 = ( y + 2 )( y - 2 )

Or,  x^2 = \frac{(y^2 - 4)}{25}

Check the options -

(A) 25x^2 + 4 = y^2 ( Possible, take 4 from LHS to RHS )
(B) 75x^2 = 3y^2 - 12 ( Possible, Multiply both the sides by 3 )
(C) C) 25x^2 = (y + 2)(y - 2) ( POssible, already worked out )
(D) 5x = y - 2 ( Not possible in any way )
(E)  x^2 = \frac{(y^2 - 4)}{25}  ( Possible already wored out )

Hence, Answer must be (D)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Which of the following Equation is NOT equivalent to 25x^2=y^2-4?

Prep Toolkit

Top 5 GMAT Debrief Videos

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Which of the following Equation is NOT equivalent to 25x^2=y^2-4?

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards