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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.

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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12 Sep 2012, 12:49

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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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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.

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.
_________________

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

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.
_________________

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

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.
_________________

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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