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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]

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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) \(y^2=\frac{(x^2-4)}{10}\)

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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]

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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]

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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]

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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]

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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]

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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]

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

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New post 12 Oct 2013, 09:33
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]

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New post 27 Oct 2014, 00:48
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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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]

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New post 07 Sep 2015, 16:57
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.


How do you actually solve using smart numbers? When I did it, all of my answers were y=0, x=2.

Let's pick x=2, when this is plugged into the equation we get y=0. So we're going to plug in 2 for all x's that we see, when y = 0 that is our answer.

a. 30y^2=3x^2-12
3(2)^2-12 = 0, therefore y=0 when x=2

b. 20y^2=(2x-4)(x+2)
(2(2)-4)(2+2) = 0, therefore y=0 when x=2

What am I doing wrong?

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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]

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New post 07 Sep 2015, 17:16
aces021 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.


How do you actually solve using smart numbers? When I did it, all of my answers were y=0, x=2.

Let's pick x=2, when this is plugged into the equation we get y=0. So we're going to plug in 2 for all x's that we see, when y = 0 that is our answer.

a. 30y^2=3x^2-12
3(2)^2-12 = 0, therefore y=0 when x=2

b. 20y^2=(2x-4)(x+2)
(2(2)-4)(2+2) = 0, therefore y=0 when x=2

What am I doing wrong?


I think you are missing out on what the question is asking. It is asking to find the expression that will NOT give you the same value as \(10y^2=(x+2)(x-2)\)

When you do use, x=2, you get the following values of 'y'

A) 0
B) 0
C) 0
D) 2/5
E) 0

From the original expression you see that when you get y=0 for x=2 for options A-C and E.

Thus, with your 'smart numbers', D is the only expression that DOES NOT give you the same values on the left hand side as those on the right hand side. D is thus the correct answer.

FYI, using smart numbers is not the best strategy for this question. You need to realize that \((A+B)(A-B) = A^2-B^2\) and thus the original expression becomes \(10y^2 = x^2-4\)

D will not give you this expression and is thus the correct answer.
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Last edited by Engr2012 on 07 Sep 2015, 19:09, edited 2 times in total.
Edited the typos, alternate reasoning

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Engr2012 wrote:
aces021 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.


How do you actually solve using smart numbers? When I did it, all of my answers were y=0, x=2.

Let's pick x=2, when this is plugged into the equation we get y=0. So we're going to plug in 2 for all x's that we see, when y = 0 that is our answer.

a. 30y^2=3x^2-12
3(2)^2-12 = 0, therefore y=0 when x=2

b. 20y^2=(2x-4)(x+2)
(2(2)-4)(2+2) = 0, therefore y=0 when x=2

What am I doing wrong?


I think you are missing out on what the question is asking. It is asking to find the expression that will NOT give you the same value as \(10y^2=(x+2)(x-2)\)

When you do use, y = 0 and x=2, you get the following

A) 15 = 15
B) 10 = 10
C) 9=9
D) 2.5 \(\neq\) 7
E) 0.5 = 0.5

From the original expression you see that when you use y=0 and x=2, you get 0=0 (LHS=RHS).

Thus, with your 'smart numbers', D is the only expression that DOES NOT give you the same values on the left hand side as those on the right hand side. D is thus the correct answer.

FYI, using smart numbers is not the best strategy for this question. You need to realize that \((A+B)(A-B) = A^2-B^2\) and thus the original expression becomes \(10y^2 = x^2-4\)

D will not give you this expression and is thus the correct answer.



Thanks for the response, how are you actually getting for a. 15=15 using x=2, y=0?

30y^2=3x^2-12
30(0)^2 = 3(2)^2 - 12

What is the order of operations? Does the above equal to
0 = 0

Or does it equal to
30*1 = 36-12
30 = 24 ?

Either way I'm not getting 15=15. Thanks!

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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]

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New post 07 Sep 2015, 19:12
aces021 wrote:


Thanks for the response, how are you actually getting for a. 15=15 using x=2, y=0?

30y^2=3x^2-12
30(0)^2 = 3(2)^2 - 12

What is the order of operations? Does the above equal to
0 = 0

Or does it equal to
30*1 = 36-12
30 = 24 ?

Either way I'm not getting 15=15. Thanks!


Sorry. I had solved this using some other set of values and wrote those values. I have updated the solution. Yes, you are correct that option A will give you y=0 for x=2. As a matter of fact, options A-C and E give y=0 when you use x=2. Option D does not and is thus the correct answer.
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]

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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]

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Bunuel wrote:
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


To solve this question, we start by FOILing the right hand side of the given equation.

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

10y^2 = x^2 – 4

We will manipulate each of the answer choices to see if it equals 10y^2 = x^2 – 4. Let’s start with A.

A) 30y^2 =3x^2 – 12

If we divide this entire equation by 3 we are left with:

10y^2 = x^2 – 4

Answer choice A is not correct.

B) 20y^2 = (2x-4)(x+2)

FOILing (2x-4)(x+2) we get:

20y^2 = 2x^2 – 8

If we divide this entire equation by 2 we obtain:

10y^2 = x^2 – 4

Answer choice B is not correct.

C) 10y^2 + 4 = x^2

If we subtract 4 from the both sides of the equation, we obtain:

10y^2 = x^2 – 4

Answer choice C is not correct.

D) 5y^2 = x^2 – 2

We should notice that no matter how we try to manipulate 5y^2 = x^2 – 2, it will never be equal to 10y^2 = x^2 – 4. For example, if we multiply both sides of 5y^2 = x^2 – 2 by 2, we will have 10y^2 = 2x^2 – 4. However, that is not the same as 10y^2 = x^2 – 4.

Answer D is correct.

To be certain, we should also test answer E.

E) y^2 = (x^2 – 4)/10

If we multiply the entire equation by 10 we obtain:

10y^2 = x^2 – 4

Answer choice E is not correct.

The answer is D.
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Re: Which of the following equations is NOT equivalent to 10y^2=   [#permalink] 25 May 2016, 09:39
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Which of the following equations is NOT equivalent to 10y^2=

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