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What is the value of x^2 - y^2? (1) x + y = 2x (2) x + y = 0

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Bunuel
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What is the value of x^2 - y^2? (1) x + y = 2x (2) x + y = 0 [#permalink] New post  11 Dec 2018, 07:32
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What is the value of x^2 - y^2?

(1) x + y = 2x
(2) x + y = 0
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Gladiator59
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Re: What is the value of x^2 - y^2? (1) x + y = 2x (2) x + y = 0 [#permalink] New post  11 Dec 2018, 08:01
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What is the value of \(x^2 - y^2\)

which simplifies to \((x+y)*(x-y)\)

So it is obvious that statement 2 is sufficient right away.

But statement 1 is tricky to miss in a hurry.

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

or

\(x - y = 0\)

Hence St 2 is also sufficient.

Hence [color=#00a651]Option (D) is our bet./color]

Best,
Gladi

Bunuel wrote:
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

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KSBGC
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Re: What is the value of x^2 - y^2? (1) x + y = 2x (2) x + y = 0 [#permalink] New post  11 Dec 2018, 08:49
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Statement 1:
x + y = 2x
x = y.

x^2 - y^2

= x^2 - x^2

= 0

Sufficient.

Statement 2:

x^2 - y^ 2

= (x+y) (x - Y)
=0 ( x - y)

= 0

Sufficient.

The best answer is D.
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Re: What is the value of x^2 - y^2? (1) x + y = 2x (2) x + y = 0 [#permalink] New post  04 Jun 2020, 06:00
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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Re: What is the value of x^2 - y^2? (1) x + y = 2x (2) x + y = 0 [#permalink] New post  13 Dec 2020, 09:32
Bunuel wrote:
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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BrentGMATPrepNow
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Re: What is the value of x^2 - y^2? (1) x + y = 2x (2) x + y = 0 [#permalink] New post  22 May 2022, 11:00
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Bunuel wrote:
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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Re: What is the value of x^2 - y^2? (1) x + y = 2x (2) x + y = 0 [#permalink] New post  16 Jul 2023, 00:03
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Re: What is the value of x^2 - y^2? (1) x + y = 2x (2) x + y = 0 [#permalink]
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