If 3x + 2y = -2z, what is x?
(1) x - y - z = 10
(2) x + y + z = -2
OA D
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If 3x + 2y = -2z, what is x?
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BTGmoderatorDC
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\[? = x\]BTGmoderatorDC wrote:If 3x + 2y = -2z, what is x?
(1) x - y - z = 10
(2) x + y + z = -2
\[3x + 2y = - 2z\,\,\,\, \Rightarrow \,\,\,\,3x = - 2\left( {y + z} \right)\,\,\,\,\,\,\left( * \right)\]
\[\left( 1 \right)\,\,\,\,x - \left( {y + z} \right) = 10\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,2} \,\,\,\,\,\,2x - 2\left( {y + z} \right) = 20\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,2x + 3x = 20\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x\,\,\,{\text{unique}}\]
\[\left( 2 \right)\,\,\,x + \left( {y + z} \right) = - 2\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,2} \,\,\,\,\,\,2x + 2\left( {y + z} \right) = - 4\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,2x - 3x = - 4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x\,\,\,{\text{unique}}\]
This solution follows the notations and rationale taught in the GMATH method.
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fskilnik.
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Prompt: 3x + 2y + 2z = 0BTGmoderatorDC wrote:If 3x + 2y = -2z, what is x?
(1) x - y - z = 10
(2) x + y + z = -2
Statement 1:
Multiplying by 2, we get:
2x - 2y - 2z = 20
Adding together 3x+2y+2z=0 and 2x-2y-2z=20, we get:
(3x+2y+2z) + (2x-2y-2z) = 0 + 20
5x=20
x=4.
SUFFICIENT.
Statement 2:
Multiplying by 2, we get:
2x + 2y + 2z = -4
Subtracting 2x+2y+2z = -4 from 3x+2y+2z=0, we get:
(3x+2y+2z) - (2x+2y+2z) = 0 - (-4)
x=4.
SUFFICIENT.
The correct answer is D.
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Brent@GMATPrepNow
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Target question: What is the value of x?BTGmoderatorDC wrote:If 3x + 2y = -2z, what is x?
(1) x - y - z = 10
(2) x + y + z = -2
Given: 3x + 2y = -2z
Notice that the two statements have the variables all on the left side of the equation. So, let's rearrange our given equation to look the same.
Take: 3x + 2y = -2z
Add 2z to both sides to get: 3x + 2y + 2z = 0
Statement 1: x - y - z = 10
Take this equation and multiply both sides by 2 to get the EQUIVALENT equation 2x - 2y - 2z = 20
So, we have:
2x - 2y - 2z = 20
3x + 2y + 2z = 0
Add the equations to get: 5x = 20
Solve: x = 4
So, the answer to the target question is x = 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x + y + z = -2
Take this equation and multiply both sides by 2 to get the EQUIVALENT equation 2x + 2y + 2z = -4
So, we have:
2x + 2y + 2z = -4
3x + 2y + 2z = 0
Subtract the bottom equation from the top equation to get:
-x = -4
Solve: x = 4
So, the answer to the target question is x = 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
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