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Which of the following equations is NOT equivalent to 10y^2= : Problem Solving (PS)
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# Which of the following equations is NOT equivalent to 10y^2=

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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

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!

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

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]
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.

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]
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

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

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]
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.

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.

Originally posted by ENGRTOMBA2018 on 07 Sep 2015, 17:16.
Last edited by ENGRTOMBA2018 on 07 Sep 2015, 19:09, edited 2 times in total.
Edited the typos, alternate reasoning
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
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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.

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]
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]
Attached is a visual that should help.
Attachments

Screen Shot 2016-05-10 at 5.50.11 PM.png [ 76.13 KiB | Viewed 35469 times ]

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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.

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.

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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Bunuel wrote:
Which of the following equations is NOT equivalent to $$10y^2=(x+2)(x-2)$$ ?

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

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