Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 45439

If x = 2t and y = t/3, what is the value of x^2 – y^2? [#permalink]
Show Tags
25 Oct 2015, 08:50
5
This post received KUDOS
Expert's post
8
This post was BOOKMARKED
Question Stats:
71% (00:59) correct 29% (00:58) wrong based on 878 sessions
HideShow timer Statistics



Current Student
Joined: 20 Mar 2014
Posts: 2644
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
2
This post received KUDOS
1
This post was BOOKMARKED
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
2
This post received KUDOS
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.



SVP
Joined: 08 Jul 2010
Posts: 2099
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!!! GMATinsight Bhoopendra 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 Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Director
Joined: 23 Jan 2013
Posts: 596

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: 62

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: 745

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: 45439

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



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11670
Location: United States (CA)
GRE 1: 340 Q170 V170

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
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************




Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?
[#permalink]
14 Dec 2017, 16:36






