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)

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

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