If x = 2t and y = t/3, what is the value

[jjjinapinch]

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

Official Guide question
Answer: D

[Brent@GMATPrepNow]

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

Official Guide question
Answer: D

Target question: What is the value of x² - y²?

Given: x = 2t and y = t/3

Statement 1: t² - 3 = 6
Add 3 to both sides to get: t² = 9
So, EITHER t = 3 OR t = -3
Let's test each case:
Case a: t = 3. Since x = 2t and y = t/3, this means x = 6 and y = 1. So, x² - y² = 6² - 1² = 36 - 1 = 35
Case b: t = -3. Since x = 2t and y = t/3, this means x = -6 and y = -1. So, x² - y² = (-6)² - (-1)² = 36 - 1 = 35
So, x² - y² MUST equal 35
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: t³ = -27
This means t = 3
Since x = 2t and y = t/3, this means x = 6 and y = 1. so, x² - y² = 6² - 1² = 36 - 1 = 35
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

[[email protected]]

Hi jjjinapinch,

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: D

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

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

Official Guide question
Answer: D

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.

Answer: D