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555-605 Level|   Algebra|      
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Bunuel
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What is the value of x – y? (1) x + y = 3y – x (2) x + y = x^3 + y^3 11 Jul 2019, 00:32
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A
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Difficulty:

25% (medium)

Question Stats:

75% (01:19) correct 25% (01:39) wrong based on 57 sessions

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What is the value of x – y?

(1) x + y = 3y – x
(2) x + y = x^3 + y^3
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A
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Neha2050
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What is the value of x – y? (1) x + y = 3y – x (2) x + y = x^3 + y^3 11 Jul 2019, 03:00
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1. 2x=2y
X=y

2. X+y=(x+y)(x2-xy +y2)
X2+y2-xy =1

IMO A

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rubythailand
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What is the value of x – y? (1) x + y = 3y – x (2) x + y = x^3 + y^3 11 Jul 2019, 04:29
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For the second choice dont forget it also means x+y could equal 0 which means x could equal -y in which case there are a host of possibilities for x-y
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What is the value of x – y? (1) x + y = 3y – x (2) x + y = x^3 + y^3 11 Jul 2019, 05:11
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Bunuel
What is the value of x – y?

(1) x + y = 3y – x
(2) x + y = x^3 + y^3

Statement (1)

\(\begin{alignat}{2}\\
&& x+y &= 3y - x\\\\
&\implies\quad &2(x-y) &= 0\\\\
&\implies\quad &x-y &= 0\\\\
\end{alignat}\)

Statement is sufficient


Statement (2)

\(\begin{alignat}{2}\\
&& x + y &= x^3 + y^3\\\\
&\implies\quad &x+y &= (x+y)(x^2-xy+y^2)\\\\
&\implies\quad &(x+y)(x^2-xy+y^2-1) &= 0\\\\
&\implies\quad &(x+y =0) \quad &or \quad (x^2-xy+y^2-1=0)\\
\end{alignat}\)

If \(x+y=0\),
\(\quad\) if \(x=-1\) and \(y=1\), then \((x-y)=-2\)
\(\quad\) if \(x=1\) and \(y=-1\), then \((x-y)=2\)

Since \((x-y)\) can have more than one value, statement is insufficient.


So, answer is A.
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Bunuel
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