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

Question

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}

Bunuel · Accepted Answer

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.

dexerash · Answer

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.

Javoni · Answer

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

fameatop · Answer

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

mbaiseasy · Answer

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= 2 x^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

runningguy · Answer

Bunuel could we also use -2??

Thanks,
C

Bunuel · Answer

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

PareshGmat · Answer

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

aces021 · Answer

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?

ENGRTOMBA2018 · Answer

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.

aces021 · 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!

ENGRTOMBA2018 · Answer

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.

mcelroytutoring · Answer

Attached is a visual that should help.

ScottTargetTestPrep · 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.

Kinshook · Answer

(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

Rebaz · Answer

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!

zaidi1212 · Answer

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

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