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

It is currently 23 May 2019, 06:03

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

If x = 2t and y = t/3, what is the value of x^2 – y^2?

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 25 Oct 2015, 08:50
6
23
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

71% (01:18) correct 29% (01:22) wrong based on 1571 sessions

HideShow timer Statistics

Most Helpful Community Reply
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2625
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 25 Oct 2015, 09:27
5
3
Bunuel wrote:
If x = 2t and y = t/3, what is the value of x^2 – y^2?

(1) t^2 – 3 = 6
(2) t^3 = −27

Kudos for a correct solution.


x=2t, y=t/3, x^2 – y^2 = ?

Per statement 1, t^2=9 ---> t= 3 or -3, after substituting both these values, you will get x^2 – y^2 = 35. Sufficient.

Per statement 2, t^3=-27 ---> t=-3, 1 value and hence you will get a unique value of x^2 – y^2. Sufficient

D is the correct choice.
General Discussion
Manager
Manager
User avatar
Joined: 22 Feb 2015
Posts: 56
Location: United States
Concentration: Finance, Operations
GMAT Date: 04-01-2015
GPA: 3.98
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 26 Oct 2015, 04:26
3
If x = 2t and y = t/3, what is the value of x^2 – y^2?

(1) t^2 – 3 = 6
(2) t^3 = −27

Sol. x^2 = 4t^2 and y^2 = t^2/9
1) t^2 = 9 so 4t^2 - t^2/9 so 36-1 = 35
2) t^3 = −27 so t = -3 and t^2=9 so 4t^2 - t^2/9 so 36-1 = 35

D Both Sufficient
_________________
Click +1 KUDOS , You can make me happy with just one click! :-) Thanks
Current Student
avatar
B
Joined: 07 Mar 2014
Posts: 192
Concentration: Leadership, Finance
Schools: Fisher '19 (A)
GPA: 3.8
WE: Information Technology (Consulting)
Reviews Badge
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 26 Oct 2015, 04:36
+1 for D
X^2 = 4t^2
Y^2 = t^2/9

Case 1:
t^2 - 3 = 6; t^2 = 9, Substitue for t^2. Sufficient.

Case :2

t^3 = -27
t = -3
t^2 = 9; Substitue for t^2. Sufficient.
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2931
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 26 Oct 2015, 06:20
1
Bunuel wrote:
If x = 2t and y = t/3, what is the value of x^2 – y^2?

(1) t^2 – 3 = 6
(2) t^3 = −27

Kudos for a correct solution.


Given : x = 2t and y = t/3

Question : x^2 – y^2=(x+y)*(x-y) = ?

Statement 1: t^2 – 3 = 6
i.e. t^2 = 9
i.e. t = +3
i.e. y =+1 respectively for respective values of t=+3
i.e. x =+6 respectively for respective values of t=+3
i.e. x^2 – y^2 = (+6)^2 - (+1)^2 = 36-1 = 35
SUFFICIENT

Statement 2: t^3 = −27
i.e. i.e. t = -3
i.e. y =-1 respectively for respective values of t=+3
i.e. x =-6 respectively for respective values of t=+3
i.e. x^2 – y^2 = (-6)^2 - (-1)^2 = 36-1 = 35
SUFFICIENT

Answer: Option D
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 549
Schools: Cambridge'16
If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 07 Jan 2016, 22:07
need to find:

(2t-1/3t)*(2t+1/3t)=(35/9)*t^2

St1. t^2=9, SUFF

St2. t=-3, SUFF

D
Intern
Intern
avatar
Joined: 08 Jan 2015
Posts: 1
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 29 Mar 2016, 07:56
Engr2012 wrote:
Bunuel wrote:
If x = 2t and y = t/3, what is the value of x^2 – y^2?

(1) t^2 – 3 = 6
(2) t^3 = −27

Kudos for a correct solution.


x=2t, y=t/3, x^2 – y^2 = ?

Per statement 1, t^2=9 ---> t= 3 or -3, after substituting both these values, you will get x^2 – y^2 = 35. Sufficient.

Per statement 2, t^3=-27 ---> t=-3, 1 value and hence you will get a unique value of x^2 – y^2. Sufficient

D is the correct choice.


Can someone explain how we solve t^3 = -27?

Do we multiply the statement by -1 such that we get: -t^3 = 27 => -t=+3 and -3?

Please clarify?
Manager
Manager
avatar
Joined: 20 Mar 2015
Posts: 58
GMAT ToolKit User
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 03 Jul 2016, 11:19
startee wrote:
Engr2012 wrote:
Bunuel wrote:
If x = 2t and y = t/3, what is the value of x^2 – y^2?

(1) t^2 – 3 = 6
(2) t^3 = −27

Kudos for a correct solution.


x=2t, y=t/3, x^2 – y^2 = ?

Per statement 1, t^2=9 ---> t= 3 or -3, after substituting both these values, you will get x^2 – y^2 = 35. Sufficient.

Per statement 2, t^3=-27 ---> t=-3, 1 value and hence you will get a unique value of x^2 – y^2. Sufficient

D is the correct choice.


Can someone explain how we solve t^3 = -27?

Do we multiply the statement by -1 such that we get: -t^3 = 27 => -t=+3 and -3?

Please clarify?


If t^odd equals to negative value k. then the number 't' has to be a negative number.

\(3^3\) \(=\) \(3*3*3 = 27\) t=3(positive number.) raised to a positive number 3.

\(-3^3\) \(=\) \(-3*-3*-3\) \(=\) \(-27\). t=-3(negative number) raised to a positive number 3.

\(3^4\) \(=\) \(-3*-3*-3*-3\) \(=\)\(81\) t = -3(negative number ) raised to a positive number 4.
Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 659
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 26 Jul 2017, 03:49
Bunuel

I went a little too far while solving this question.

I got:
(7t/3) (5t/3)

From statement 1: t^2= 9
So t can be positive 3 or negative 3.

When I plugged in the value the answer was 35 in both the cases..

My query is when we get the same answer, do we have to worry about the two values of t because we usually take one?
Or we have to just consider unique value of x^2-y^2?


Also when its given that t^3= -27

We have to just take the negative because (negative)^odd = negative

and we have to take both positive and negative values into consideration when its (value)^even....
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Intern
Intern
avatar
Joined: 27 Apr 2015
Posts: 8
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 25 Sep 2017, 17:42
If the question prompt wanted (x^3 - y^3) or (x - y) rather than (X^2 - y^2)

then statement 1 would not be sufficient, correct?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 25 Sep 2017, 21:10
1
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14194
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 14 Dec 2017, 16:36
Hi All,

Certain DS questions are really just a 'test' of your 'thoroughness', so it's important to do all of the necessary work (on the pad; NOT 'in your head') to prove what the correct answer is. Without having that 'proof', you might inadvertently choose the wrong answer (and miss out on some easy points on Test Day).

We're told that X = 2T and Y = T/3. We're asked for the value of X^2 - Y^2

1) T^2 - 3 = 6.

With the equation in Fact 1, we can determine that T has 2 values...
T^2 - 3 = 6
T^2 = 9
T = +3 or -3
Many Test Takers would assume that these two values would lead to two different answers to the question (and assume that Fact 1 was insufficient).... but where is your PROOF that it's insufficient...?

IF....
T = 3, X=6, Y=1, then the answer to the question is 6^2 - 1^2 = 35
IF....
T = -3, X= -6, Y= -1, then the answer to the question is (-6)^2 - (-1)^2 = 35
It turns out that both values of T lead to the SAME answer - and the answer to the question is ALWAYS 35.
Fact 1 is SUFFICIENT

2) t^3 = -27

The equation in Fact 2 has just one solution: -3. With the work that we did in Fact 1, we know that there is only one answer to the question (35).
Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Manager
Manager
User avatar
G
Joined: 21 Jun 2017
Posts: 234
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 06 Jan 2019, 06:15
Ok. Was just wondering. Some irrational's irrational power can equal -27. In this case t may not be -3

Please guide.
_________________
Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Dil ye Ziddi hai !!!
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14194
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

Show Tags

New post 06 Jan 2019, 13:22
1
ShankSouljaBoi wrote:
Ok. Was just wondering. Some irrational's irrational power can equal -27. In this case t may not be -3

Please guide.


Hi ShankSouljaBoi,

The information in Fact 1 and Fact 2 defines specific 'powers' (a square and a cube), so there's no possibility of an 'irrational power.'

Assuming that you are focusing on Fact 2, we know that there is a CUBED number that equals - 27. By definition, that number MUST be NEGATIVE...

(positive)^3 = positive
(0)^3 = 0
(negative)^3 = negative

In addition, increasing or decreasing the value of the negative will change the value of the cubed term...

(-2)^3 = -8
(-3)^3 = -27
(-4)^3 = -64
Etc.

Thus, even if you are changing the number in really small increments (for example -3 vs -2.999 or -3.1), the end cubed value will change (meaning that there's ONLLY ONE way to get to a -27 result.... when we use -3).

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
GMAT Club Bot
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?   [#permalink] 06 Jan 2019, 13:22
Display posts from previous: Sort by

If x = 2t and y = t/3, what is the value of x^2 – y^2?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.