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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

Kudos for a correct solution.
[Reveal] Spoiler: OA

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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
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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
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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19 Jul 2017, 23:52
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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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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
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] 25 Sep 2017, 21:10
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