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23 May 2020, 08:49
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B
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If \(x^2 + 5z + 2xy + 6 = 2xy\) and \(x ≠ –2\), what is the value of x ?
(1) \(y = 1\)
(2) \(z = x\)
DS20436
(1) \(y = 1\)
(2) \(z = x\)
DS20436
23 May 2020, 09:30
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Bunuel
If \(x^2 + 5z + 2xy + 6 = 2xy\) and \(x ≠ –2\), what is the value of x ?
(1) \(y = 1\)
(2) \(z = x\)
DS20436
Target question: What is the value of x ?(1) \(y = 1\)
(2) \(z = x\)
DS20436
Given: x² + 5z + 2xy + 6 = 2xy
Subtract 2xy from both sides of the equation to get: x² + 5z + 6 = 0
At this point, we can see that, in order to find the value of x, we'll first need to know the value of z
Statement 1: y = 1
Since we're now dealing with the equation x² + 5z + 6 = 0, the value of y is irrelevant
Statement 1 is NOT SUFFICIENT
Statement 2: z = x
Take: x² + 5z + 6 = 0
Replace z with x to get: x² + 5x + 6 = 0
Factor to get: (x + 2)(x + 3) = 0
So, EITHER x = -2 OR x = -3
At this point, we might incorrectly conclude that statement 2 is not sufficient (since we have two different possible values of x).
However, the given information tells us that x ≠ –2
So, it must be the case that x = -3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
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23 May 2020, 09:39
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Answer is B
X^2+5Z+2XY+6=2XY
X^2+5Z+6=0
Statement 1 : Y=1
Nothing given regarding X (not sufficient)
Statement 2: x=z
X^2+5Z+6=0
X^2+5X+6=0
X^2+2X+3X+6=0
(X+2)(X+3)=0
X=-2,&-3
Since x≠-2
X=-3 (sufficient)
Posted from my mobile device
X^2+5Z+2XY+6=2XY
X^2+5Z+6=0
Statement 1 : Y=1
Nothing given regarding X (not sufficient)
Statement 2: x=z
X^2+5Z+6=0
X^2+5X+6=0
X^2+2X+3X+6=0
(X+2)(X+3)=0
X=-2,&-3
Since x≠-2
X=-3 (sufficient)
Posted from my mobile device
