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

Apparently (D), since after dividing by 2, we should get 5y^2=(x^2-4)/2

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

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

Bunuel could we also use -2??

Thanks,
C

Yes we can. We can use the same exact logic.

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

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.

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.

Attached is a visual that should help.

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.

(A) \(30y^2=3x^2-12\)
3*equation
(B) \(20y^2=(2x-4)(x+2)\)
2*equation
(C) \(10y^2+4=x^2\)
Equation
(D) \(5y^2=x^2-2\)
10y^2 = 2x^2-4
NOT THE EQUATION
(E) \(y^2=\frac{(x^2-4)}{10}\)
Equation/10

IMO D

Posted from my mobile device

Can someone please explain me where i go wrong with the process called FOIL (First, Outer, Inner, and Last)?

Here is how i do it according to Manhattan Gmat:

For example: (A+B)(A−B)=

First-------------(A*A)=A^2
Outer----------- (A*-B)= -AB
Inner------------(A*B)=+ AB
Last-------------(B*-B)=-B^2

Finally we get: A^2 - AB + AB -B^2= A^2 - B^2 (-AB and + AB cancel each other out in the addition process)

If i perform the exact same FOIL steps for the right side of choice B, 20y^2 = (2x-4)(x+2), then i get the following:

(2x-4)(x+2)=

First-------------(2x*x)=2X^2
Outer----------- (X*2)= 2X
Inner------------(2X*-4)=-8X
Last-------------(-4*2)=-8

Finally we get: 2X^2 + 2X - 8X - 8 = 2X^2 -6X - 8.

Where do i go wrong here?

I see that when other folks apply the FOIL process to the right side of option B, they get: 2x^2 – 8, which is different from my solution for the right side of option B.

This is how other folks have done it.

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

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

20y^2 = 2x^2 – 8



Please help!!!

Thanks in advanced!

Question: Which of the following is not equal to 10y2 = x2 -4

Clearly it is D because:
(D) 5y2=x2−2
-> 10y2 = 2x2 - 4 which can't be equal to 10y2 = x2 -4

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