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Math Expert V
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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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Difficulty:   25% (medium)

Question Stats: 73% (01:19) correct 27% (01:20) wrong based on 1962 sessions

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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.

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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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8
3
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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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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+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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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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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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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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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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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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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: 65785
Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?  [#permalink]

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

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Ok. Was just wondering. Some irrational's irrational power can equal -27. In this case t may not be -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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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).

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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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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.

If x = 2t and y = t/3, what is the value of x^2 – y^2?
$$x^2 – y^2 = 4t^2 - t^2/9 = 35t^2/9$$

(1) t^2 – 3 = 6
t^2 = 9
35t^2/9 = 35
SUFFICIENT

(2) t^3 = −27
$$t^3 = -27$$
t = -3
$$35t^2/9 = 35*(-3)^2/9 = 35$$
SUFFICIENT

IMO D
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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.

Need value of t but we need to make that all values of t give the same answer.

1) t^2 = 9 => Sufficient since t^2 is enough

2) t = - 3 => Sufficient Re: If x = 2t and y = t/3, what is the value of x^2 – y^2?   [#permalink] 23 Mar 2020, 04:15

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