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Bunuel
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What is the value of x^2 - y^2?

(1) x + y = 2x

x + y=2x -----> y = 2x - x -----> y=x

If we substitute y=x back into the main expression, we get (x^2) - (y^2) ---> (x^2) - (x^2)= 0
Therefore, (1) alone is sufficient

Now, let us analyze (2).

(2) x + y = 0

recall the main expression: x^2 - y^2

x^2 - y^2 ----> (x+y)(x-y). This is the simplified version of the main expression.

If we substitute (2) into this main expression, we get:

(x+y)(x-y) ----> (0)*(x-y) = 0.
Therefore, using (2) alone, we were able to find a unique value.
Hence, (2) alone is sufficient

Since (1) and (2) alone are sufficient, the correct answer is (D).
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Bunuel
What is the value of x^2 - y^2?

(1) x + y = 2x
(2) x + y = 0


Project DS Butler: Day 36: Data Sufficiency (DS71)


For DS butler Questions Click Here

What is (x+y)(x-y)?

(1) \(x + y = 2x\)
\(y = x \)
\(x - y = 0 \)

SUFFICIENT

(2) \(x + y = 0 \)

SUFFICIENT

Answer is D.
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Bunuel
What is the value of x² - y²?

(1) x + y = 2x
(2) x + y = 0

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

Statement 1: x + y = 2x
Subtract x from both sides of the equation: y = x
Now take the target question and replace x with y to get: What is the value of y² - y²?
At this point, it's obvious that x² - y² = y² - y² = 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x + y = 0
Since the target question, x² - y², is a difference of squares, we're really trying to find the value of (x + y)(x - y)
Since we're told x + y = 0, we can substitute this into the target question to get:
So, x² - y² = (x + y)(x - y) = (0)(x - y) = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D
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What is the value of x^2 - y^2?

(1) x + y = 2x
(2) x + y = 0

Statement 1:
y=x thus x^2 = y^2

Statement 2:
x = -y thus x^2 = y^2

Thus D
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