Last visit was: 03 Aug 2024, 05:56 It is currently 03 Aug 2024, 05:56
Toolkit
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.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94776
Own Kudos [?]: 646242 [75]
Given Kudos: 86843
SVP
Joined: 20 Mar 2014
Posts: 2356
Own Kudos [?]: 3653 [13]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 1754 [4]
Given Kudos: 66
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
General Discussion
Manager
Joined: 22 Feb 2015
Posts: 54
Own Kudos [?]: 166 [4]
Given Kudos: 3
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]
4
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 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
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6051
Own Kudos [?]: 13873 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2? [#permalink]
1
Kudos
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

Intern
Joined: 27 Apr 2015
Posts: 6
Own Kudos [?]: 6 [1]
Given Kudos: 2
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2? [#permalink]
1
Kudos
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: 94776
Own Kudos [?]: 646242 [3]
Given Kudos: 86843
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2? [#permalink]
3
Kudos
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.
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11811 [2]
Given Kudos: 450
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]
2
Kudos
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

GMAT assassins aren't born, they're made,
Rich
Director
Joined: 21 Jun 2017
Posts: 632
Own Kudos [?]: 541 [0]
Given Kudos: 4092
Location: India
Concentration: Finance, Economics
GMAT 1: 660 Q49 V31
GMAT 2: 620 Q47 V30
GMAT 3: 650 Q48 V31
GPA: 3.1
WE:Corporate Finance (Non-Profit and Government)
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2? [#permalink]
Ok. Was just wondering. Some irrational's irrational power can equal -27. In this case t may not be -3

GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11811 [1]
Given Kudos: 450
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]
1
Kudos
ShankSouljaBoi wrote:
Ok. Was just wondering. Some irrational's irrational power can equal -27. In this case t may not be -3

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
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6051
Own Kudos [?]: 13873 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2? [#permalink]
1
Kudos
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.

Wanna make solving the Official Questions interesting???

Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course

Video solution by GMATinsight

Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub
Intern
Joined: 29 Apr 2021
Posts: 48
Own Kudos [?]: 20 [0]
Given Kudos: 51
Location: India
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2? [#permalink]
To make the solution easy lets solve the equation in the question first:
putting the values of x and y in the equation we will get:
x^2-y^2= (35t^2)/9

Statement 1 : SUFFICIENT as it gives the value for t which is enough to find the value for x^2-y^2
Statement 2 : SUFFICIENT as it gives the value for t which is enough to find the value for x^2-y^2

Intern
Joined: 03 May 2021
Posts: 37
Own Kudos [?]: 13 [0]
Given Kudos: 13
Location: Kuwait
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2? [#permalink]
I had put down statement (1) as insufficient because, given t = +/- 3, I had possible values of X as +/- 6 and for Y +/- 1. But when I plug this different values in the equation that we are trying to prove (x+y)(x-y), I got different answers. Sometimes I would get 35, other times I would get -35. Therefore I had selected (1) as sufficient.

For example:
Y = 1 or -1
X = 6 or -6

Test into equation (x+y)(x-y) to make sure we get the same outcomes.

Test 1: X = 6, Y = 1
(7)(5) = 35

Test 2: X = 6, Y = -1
(5)(7) = 35

Test 3: X = -6, Y = -1
(-7)(-5) = 35

Test 4: X = -6, Y = 1
(-5)(-7) = 35

Oh, wait.... nvm - they all result in 35 - must've been a calculation error... Lol!
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19249
Own Kudos [?]: 22783 [1]
Given Kudos: 286
Location: United States (CA)
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2? [#permalink]
1
Bookmarks
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.

Solution:

We need to determine the value of x^2 - y^2 given that x = 2t and y = t/3. Substituting 2t for x and t/3 for y, we have:

(2t)^2 - (t/3)^2 = 4t^2 - t^2/9 = 35t^2 / 9

Therefore, if we can determine the value of t, we can determine the value of x^2 - y^2 since it’s equal to 35t^2 / 9.

Statement One Alone:

Solving the equation, we have:

t^2 = 9

t = ±√9

t = ±3

Although the value of t is not unique (it can be either 3 or -3), we see that t^2 = 9, regardless of whether t is 3 or -3. Thus, the value of x^2 - y^2 is 35(9) / 9 = 35. Statement one alone is sufficient.

Statement Two Alone:

Solving the equation, we have:

t^3 = -27

t = ∛(-27)

t = -3

Since t = -3, the value of x^2 - y^2 is [35(-3)^2]/9 = 35(9)/35 = 35. Statement two alone is sufficient.

Intern
Joined: 29 Apr 2021
Posts: 48
Own Kudos [?]: 20 [0]
Given Kudos: 51
Location: India
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2? [#permalink]
4t^2- t^2/9
[t^2(36-1)]/9
35t^2/9

Now using st 1 and st 2 individually w can find the value
Non-Human User
Joined: 09 Sep 2013
Posts: 34223
Own Kudos [?]: 857 [0]
Given Kudos: 0
Re: If x = 2t and y = t/3, what is the value of x^2 y^2? [#permalink]
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.
Re: If x = 2t and y = t/3, what is the value of x^2 y^2? [#permalink]
Moderator:
Math Expert
94776 posts