GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 20:55 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Which of the following equations is NOT equivalent to 10y^2=

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58322
Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

2
16 00:00

Difficulty:   5% (low)

Question Stats: 84% (01:22) correct 16% (01:25) wrong based on 1503 sessions

HideShow timer Statistics

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) $$y^2=\frac{(x^2-4)}{10}$$

Practice Questions
Question: 37
Page: 157
Difficulty: 600

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58322
Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

11
6
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.

_________________
Manager  Joined: 12 Mar 2012
Posts: 99
Location: India
Concentration: Technology, General Management
GMAT Date: 07-23-2012
WE: Programming (Telecommunications)
Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

7
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.
_________________
FOCUS..this is all I need!

Ku-Do!
General Discussion
Intern  Status: Life begins at the End of your Comfort Zone
Joined: 31 Jul 2011
Posts: 41
Location: Tajikistan
Concentration: General Management, Technology
GPA: 3.86
Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

2
Apparently (D), since after dividing by 2, we should get 5y^2=(x^2-4)/2
_________________
God loves the steadfast.
Senior Manager  B
Joined: 24 Aug 2009
Posts: 446
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

3
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
_________________
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: 401
Concentration: Marketing, Finance
GPA: 3.23
Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

3
1
$$10y^2=(x+2)(x-2)$$ 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!

_________________
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

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
Math Expert V
Joined: 02 Sep 2009
Posts: 58322
Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

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.
_________________
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1751
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

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

_________________
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

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?
CEO  S
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

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
Intern  Joined: 16 Feb 2015
Posts: 9
Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

1
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!
CEO  S
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

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.
Director  P
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 706
Location: United States (CA)
Age: 39
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42 GRE 1: Q168 V169 WE: Education (Education)
Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

Attached is a visual that should help.
Attachments Screen Shot 2016-05-10 at 5.50.11 PM.png [ 76.13 KiB | Viewed 17796 times ]

_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching 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.

You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y7knw7bt Date of Birth: 09 December 1979.

GMAT Action Plan and Free E-Book - McElroy Tutoring

Contact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club) or find me on reddit: http://www.reddit.com/r/GMATpreparation
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8043
Location: United States (CA)
Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

1
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.

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.
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

SVP  P
Joined: 03 Jun 2019
Posts: 1684
Location: India
Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

Show Tags

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
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com Re: Which of the following equations is NOT equivalent to 10y^2=   [#permalink] 15 Sep 2019, 06:32
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  