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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] New post 11 Sep 2012, 03:37
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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

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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 11 Sep 2012, 03:38
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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] New post 11 Sep 2012, 05:20
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Bunuel wrote:
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

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Question: 37
Page: 157
Difficulty: 600


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Its D.. it should be.. 5y^2=X^2/2-2
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 11 Sep 2012, 08:07
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Bunuel wrote:
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] New post 11 Sep 2012, 08:19
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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] New post 12 Sep 2012, 11:49
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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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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 14 Sep 2012, 04:33
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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.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 14 Sep 2012, 04:51
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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.


Kudos points given to everyone with correct solution. Let me know if I missed someone.



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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 10 Dec 2012, 00:14
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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^2Exactly 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] New post 12 Oct 2013, 08:09
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,
C
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Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink] New post 12 Oct 2013, 08:33
Expert's post
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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Which of the following equations is NOT equivalent to 10y^2=   [#permalink] 12 Oct 2013, 08:33
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