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

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

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25 Oct 2015, 08:50
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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

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

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25 Oct 2015, 09:27
5
2
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.
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Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

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26 Oct 2015, 04:26
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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
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Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

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

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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

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

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

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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?

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

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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?

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

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

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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?
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Posts: 53657
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

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25 Sep 2017, 21:10
1
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.
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Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

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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

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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!***** 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/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13755 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 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 Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?   [#permalink] 06 Jan 2019, 13:22
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