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Which of the following equations is NOT equivalent to 10y^2=

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Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 11 Sep 2012, 03:37
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Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x-2)\) ?

(A) 30y^2=3x^2-12
(B) 20y^2=(2x-4)(x+2)
(C) 10y^2+4=x^2
(D) 5y^2=x^2-2
(E) y^2=(x^2-4)/10

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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 11 Sep 2012, 03:38
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SOLUTION

Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x-2)\) ?

(A) 30y^2=3x^2-12
(B) 20y^2=(2x-4)(x+2)
(C) 10y^2+4=x^2
(D) 5y^2=x^2-2
(E) y^2=(x^2-4)/10

When \(x=2\), then \(10y^2=(2+2)(2-2)=0\) --> \(y=0\).

Now, plug \(x=2\) into the answer choices and look for the option which does not give \(y=0\). Only option D gives the value of \(y\) different from zero.

Answer: D.
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 11 Sep 2012, 05:20
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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x-2)\) ?

(A) 30y^2=3x^2-12
(B) 20y^2=(2x-4)(x+2)
(C) 10y^2+4=x^2
(D) 5y^2=x^2-2
(E) y^2=(x^2-4)/10

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Question: 37
Page: 157
Difficulty: 600


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Its D.. it should be.. 5y^2=X^2/2-2
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 11 Sep 2012, 08:07
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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x-2)\) ?

(A) 30y^2=3x^2-12
(B) 20y^2=(2x-4)(x+2)
(C) 10y^2+4=x^2
(D) 5y^2=x^2-2
(E) y^2=(x^2-4)/10



A) dividing by 3 on either side gives the same equation as given in question stem ==> 3* 10y^2=3(x^2-4) ==> 3* 10^y = 3(x + 2)(x - 2) ==> Q
B) diving by 2 on both side ==> 2* 10y^2=2 * (x-2)(x+2) ==> Q
C) taking 4 to right hand side and solving ==> 10y^2=x^2 - 4 ==> 10y^2 = (x+2)(x-2) ==> Q
D) multiplying both side by 2 ==> 10y^2=2x^2-4 ==> left hand side can't be factored to (x-2)(x+2). Hence, this is NOT equivalent to equation given in Q stem.
We can stop here and mark option D.
E) multiply both sides by 10 ==> 10 y^2=10 *(x^2-4)/10 ==> 10 y^2=(x^2-4) ==> 10 y^2=(x+2)(x-2)


** basic formula which should be known prior to solving this question =====> (A^2 - B^2) = (A+B)(A-B)


Other method to solve this Q is by substituting the values. The best value to take for "x" is 2 as it will make right hand side of the equation ZERO.
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 11 Sep 2012, 08:19
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Apparently (D), since after dividing by 2, we should get 5y^2=(x^2-4)/2
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 12 Sep 2012, 11:49
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Which of the following equations is NOT equivalent to 10y^2=(x+2)(x-2) ?
(A) 30y^2=3x^2-12
(B) 20y^2=(2x-4)(x+2)
(C) 10y^2+4=x^2
(D) 5y^2=x^2-2
(E) y^2=(x^2-4)/10

The original equation reduces to 10y^2 = x^2 -4
Option 1 - 3 times of equation
Option 2 - 2 times of equation
Option 3 - Same as original of equation
Option 4 - Answer (Skip this option & jump to option 5, which in turn is right. Thus using POE this will be the answer. To cross check one can solve it)
Option 5 - 1/10 times of equation
Answer D

Hope it helps
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 14 Sep 2012, 04:33
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SOLUTION

Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x-2)\) ?

(A) 30y^2=3x^2-12
(B) 20y^2=(2x-4)(x+2)
(C) 10y^2+4=x^2
(D) 5y^2=x^2-2
(E) y^2=(x^2-4)/10

When \(x=2\), then \(10y^2=(2+2)(2-2)=0\) --> \(y=0\).

Now, plug \(x=2\) into the answer choices and look for the option which does not give \(y=0\). Only option D gives the value of \(y\) different from zero.

Answer: D.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 14 Sep 2012, 04:51
Bunuel wrote:
SOLUTION

Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x-2)\) ?

(A) 30y^2=3x^2-12
(B) 20y^2=(2x-4)(x+2)
(C) 10y^2+4=x^2
(D) 5y^2=x^2-2
(E) y^2=(x^2-4)/10

When \(x=2\), then \(10y^2=(2+2)(2-2)=0\) --> \(y=0\).

Now, plug \(x=2\) into the answer choices and look for the option which does not give \(y=0\). Only option D gives the value of \(y\) different from zero.

Answer: D.


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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 10 Dec 2012, 00:14
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\(10y^2=(x+2)(x-2)\) expands as \(10y^2=x^2-4\)

(A) \(30y^2=3x^2-12\)
Divide by 3 yields \(10y^2=x^2-4\)
Eliminate!


(B) \(20y^2=(2x-4)(x+2)\) expands as \(20y2=2x^2-8\)
Divide by 2 yields \(10y^2 = x^2-4\)
Eliminate!


(C) \(10y^2+4=x^2\)Exactly the orginal.
Eliminate!


(D) \(5y^2=x^2-2\)
Multiply by 2 expands as \(10y^2=2x^2-4\)
It's totally different!

(E) \(y^2=\frac{{x^2-4}}{{10}}\)
Multiply by 10 expands as \(10y^2=x^2-4\)
Eliminate!


Answer: D
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 12 Oct 2013, 08:09
Bunuel wrote:
SOLUTION

Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x-2)\) ?

(A) 30y^2=3x^2-12
(B) 20y^2=(2x-4)(x+2)
(C) 10y^2+4=x^2
(D) 5y^2=x^2-2
(E) y^2=(x^2-4)/10

When \(x=2\), then \(10y^2=(2+2)(2-2)=0\) --> \(y=0\).

Now, plug \(x=2\) into the answer choices and look for the option which does not give \(y=0\). Only option D gives the value of \(y\) different from zero.

Answer: D.


Bunuel could we also use -2??

Thanks,
C
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 12 Oct 2013, 08:33
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runningguy wrote:
Bunuel wrote:
SOLUTION

Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x-2)\) ?

(A) 30y^2=3x^2-12
(B) 20y^2=(2x-4)(x+2)
(C) 10y^2+4=x^2
(D) 5y^2=x^2-2
(E) y^2=(x^2-4)/10

When \(x=2\), then \(10y^2=(2+2)(2-2)=0\) --> \(y=0\).

Now, plug \(x=2\) into the answer choices and look for the option which does not give \(y=0\). Only option D gives the value of \(y\) different from zero.

Answer: D.


Bunuel could we also use -2??

Thanks,
C


Yes we can. We can use the same exact logic.
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 26 Oct 2014, 05:14
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Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 26 Oct 2014, 23:48
One good thing of this question is that \(y^2\) term is on LHS of the question as well as all 5 options given.

\(10y^2 = (x+2)(x-2)\)

For y = 0, x = 2 (Ignore -ve sign aspect)

Placing value of y = 0 in the OA

A: \(3x^2 - 12 = 0; x = 2\)

B: (2x-4)(x+2) = 0; x = 2

C: \(x^2 = 4; x = 2\)

D:\(x^2 - 2 = 0; x = \sqrt{2}\) >> Does not stand >> This is the answer

E: Same as option C

Answer = D
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Which of the following equations is NOT equivalent to 10y^2=   [#permalink] 26 Oct 2014, 23:48
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