Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46129

Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
11 Sep 2012, 04:37
Question Stats:
81% (01:04) correct 19% (01:00) wrong based on 1501 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 46129

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
11 Sep 2012, 04:38



Manager
Joined: 12 Mar 2012
Posts: 144
Location: India
Concentration: Technology, General Management
GMAT Date: 07232012
WE: Programming (Telecommunications)

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
11 Sep 2012, 09:07
Bunuel wrote: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectWhich of the following equations is NOT equivalent to \(10y^2=(x+2)(x2)\) ? (A) 30y^2=3x^212 (B) 20y^2=(2x4)(x+2) (C) 10y^2+4=x^2 (D) 5y^2=x^22 (E) y^2=(x^24)/10 A) dividing by 3 on either side gives the same equation as given in question stem ==> 3* 10y^2=3(x^24) ==> 3* 10^y = 3(x + 2)(x  2) ==> Q B) diving by 2 on both side ==> 2* 10y^2=2 * (x2)(x+2) ==> Q C) taking 4 to right hand side and solving ==> 10y^2=x^2  4 ==> 10y^2 = (x+2)(x2) ==> Q D) multiplying both side by 2 ==> 10y^2=2x^24 ==> left hand side can't be factored to (x2)(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^24)/10 ==> 10 y^2=(x^24) ==> 10 y^2=(x+2)(x2) ** basic formula which should be known prior to solving this question =====> (A^2  B^2) = (A+B)(AB) 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.
_________________
FOCUS..this is all I need!
KuDo!



Intern
Status: Life begins at the End of your Comfort Zone
Joined: 31 Jul 2011
Posts: 45
Location: Tajikistan
Concentration: General Management, Technology
GPA: 3.86

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
11 Sep 2012, 09:19
Apparently (D), since after dividing by 2, we should get 5y^2=(x^24)/2
_________________
God loves the steadfast.



Senior Manager
Joined: 24 Aug 2009
Posts: 481
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
12 Sep 2012, 12:49
Which of the following equations is NOT equivalent to 10y^2=(x+2)(x2) ? (A) 30y^2=3x^212 (B) 20y^2=(2x4)(x+2) (C) 10y^2+4=x^2 (D) 5y^2=x^22 (E) y^2=(x^24)/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
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth Game Theory
If you have any question regarding my post, kindly pm me or else I won't be able to reply



Senior Manager
Joined: 13 Aug 2012
Posts: 443
Concentration: Marketing, Finance
GPA: 3.23

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
10 Dec 2012, 01:14
\(10y^2=(x+2)(x2)\) expands as \(10y^2=x^24\) (A) \(30y^2=3x^212\) Divide by 3 yields \(10y^2=x^24\) Eliminate!(B) \(20y^2=(2x4)(x+2)\) expands as \(20y2=2x^28\) Divide by 2 yields \(10y^2 = x^24\) Eliminate!(C) \(10y^2+4=x^2\) Exactly the orginal. Eliminate!(D) \(5y^2=x^22\) Multiply by 2 expands as \(10y^2= 2x^24\) It's totally different! (E) \(y^2=\frac{{x^24}}{{10}}\) Multiply by 10 expands as \(10y^2=x^24\) Eliminate!Answer: D
_________________
Impossible is nothing to God.



Intern
Joined: 09 Sep 2013
Posts: 16

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
12 Oct 2013, 09:09
Bunuel wrote: SOLUTION
Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x2)\) ?
(A) 30y^2=3x^212 (B) 20y^2=(2x4)(x+2) (C) 10y^2+4=x^2 (D) 5y^2=x^22 (E) y^2=(x^24)/10
When \(x=2\), then \(10y^2=(2+2)(22)=0\) > \(y=0\).
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



Math Expert
Joined: 02 Sep 2009
Posts: 46129

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
12 Oct 2013, 09:33



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
27 Oct 2014, 00:48
One good thing of this question is that \(y^2\) term is on LHS of the question as well as all 5 options given. \(10y^2 = (x+2)(x2)\) 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: (2x4)(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 answerE: Same as option C Answer = D
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 16 Feb 2015
Posts: 9

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
07 Sep 2015, 16:57
Bunuel wrote: SOLUTION
Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x2)\) ?
(A) 30y^2=3x^212 (B) 20y^2=(2x4)(x+2) (C) 10y^2+4=x^2 (D) 5y^2=x^22 (E) y^2=(x^24)/10
When \(x=2\), then \(10y^2=(2+2)(22)=0\) > \(y=0\).
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^212 3(2)^212 = 0, therefore y=0 when x=2 b. 20y^2=(2x4)(x+2) (2(2)4)(2+2) = 0, therefore y=0 when x=2 What am I doing wrong?



Current Student
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
Updated on: 07 Sep 2015, 19:09
aces021 wrote: Bunuel wrote: SOLUTION
Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x2)\) ?
(A) 30y^2=3x^212 (B) 20y^2=(2x4)(x+2) (C) 10y^2+4=x^2 (D) 5y^2=x^22 (E) y^2=(x^24)/10
When \(x=2\), then \(10y^2=(2+2)(22)=0\) > \(y=0\).
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^212 3(2)^212 = 0, therefore y=0 when x=2 b. 20y^2=(2x4)(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 \(10y^2=(x+2)(x2)\) 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 AC 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 \((A+B)(AB) = A^2B^2\) and thus the original expression becomes \(10y^2 = x^24\) 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



Intern
Joined: 16 Feb 2015
Posts: 9

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
07 Sep 2015, 19:05
Engr2012 wrote: aces021 wrote: Bunuel wrote: SOLUTION
Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x2)\) ?
(A) 30y^2=3x^212 (B) 20y^2=(2x4)(x+2) (C) 10y^2+4=x^2 (D) 5y^2=x^22 (E) y^2=(x^24)/10
When \(x=2\), then \(10y^2=(2+2)(22)=0\) > \(y=0\).
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^212 3(2)^212 = 0, therefore y=0 when x=2 b. 20y^2=(2x4)(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 \(10y^2=(x+2)(x2)\) 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 \(\neq\) 7E) 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 \((A+B)(AB) = A^2B^2\) and thus the original expression becomes \(10y^2 = x^24\) 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^212 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 = 3612 30 = 24 ? Either way I'm not getting 15=15. Thanks!



Current Student
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
07 Sep 2015, 19:12
aces021 wrote:
Thanks for the response, how are you actually getting for a. 15=15 using x=2, y=0?
30y^2=3x^212 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 = 3612 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 AC and E give y=0 when you use x=2. Option D does not and is thus the correct answer.



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 645
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
GRE 1: 337 Q168 V169
WE: Education (Education)

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
10 May 2016, 18:11
Attached is a visual that should help.
Attachments
Screen Shot 20160510 at 5.50.11 PM.png [ 76.13 KiB  Viewed 10842 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both inperson (San Diego, CA, USA) and online worldwide, since 2002.
One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).
You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y8zh6qby Date of Birth: 09 December 1979.
GMAT Action Plan and Free EBook  McElroy Tutoring



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2738
Location: United States (CA)

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
25 May 2016, 09:39
Bunuel wrote: Which of the following equations is NOT equivalent to \(10y^2=(x+2)(x2)\) ?
(A) 30y^2=3x^212 (B) 20y^2=(2x4)(x+2) (C) 10y^2+4=x^2 (D) 5y^2=x^22 (E) y^2=(x^24)/10 To solve this question, we start by FOILing the right hand side of the given equation. 10y^2 = (x+2)(x2) 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 – 12If 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 = (2x4)(x+2)FOILing (2x4)(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^2If 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 – 2We 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)/10If we multiply the entire equation by 10 we obtain: 10y^2 = x^2 – 4 Answer choice E is not correct. The answer is D.
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



NonHuman User
Joined: 09 Sep 2013
Posts: 6998

Re: Which of the following equations is NOT equivalent to 10y^2= [#permalink]
Show Tags
04 Feb 2018, 09:20
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Which of the following equations is NOT equivalent to 10y^2=
[#permalink]
04 Feb 2018, 09:20






