May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27
Author 
Message 
TAGS:

Hide Tags

Math Expert
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
25 Oct 2015, 08:50
Question Stats:
71% (01:18) correct 29% (01:22) wrong based on 1571 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




CEO
Joined: 20 Mar 2014
Posts: 2625
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?
[#permalink]
Show Tags
25 Oct 2015, 09:27
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.




Manager
Joined: 22 Feb 2015
Posts: 56
Location: United States
Concentration: Finance, Operations
GMAT Date: 04012015
GPA: 3.98

Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?
[#permalink]
Show Tags
26 Oct 2015, 04:26
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 361 = 35 2) t^3 = −27 so t = 3 and t^2=9 so 4t^2  t^2/9 so 361 = 35 D Both Sufficient
_________________
Click +1 KUDOS , You can make me happy with just one click! Thanks



Current Student
Joined: 07 Mar 2014
Posts: 192
Concentration: Leadership, Finance
GPA: 3.8
WE: Information Technology (Consulting)

Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?
[#permalink]
Show Tags
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
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2931
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?
[#permalink]
Show Tags
26 Oct 2015, 06:20
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/3Question : x^2 – y^2=(x+y)*(xy) = ?Statement 1: t^2 – 3 = 6i.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 = 361 = 35 SUFFICIENT Statement 2: t^3 = −27i.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 = 361 = 35 SUFFICIENT Answer: Option D
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Director
Joined: 23 Jan 2013
Posts: 549

If x = 2t and y = t/3, what is the value of x^2 – y^2?
[#permalink]
Show Tags
07 Jan 2016, 22:07
need to find:
(2t1/3t)*(2t+1/3t)=(35/9)*t^2
St1. t^2=9, SUFF
St2. t=3, SUFF
D



Intern
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
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
Joined: 20 Mar 2015
Posts: 58

Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?
[#permalink]
Show Tags
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
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
26 Jul 2017, 03:49
BunuelI 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^2y^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
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
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
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
25 Sep 2017, 21:10
ThisandThat wrote: 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? Yes. In this case the answer would be B.
_________________



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14194
Location: United States (CA)

Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?
[#permalink]
Show Tags
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
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/



Manager
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
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
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14194
Location: United States (CA)

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




Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?
[#permalink]
06 Jan 2019, 13:22






