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Bunuel
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Bunuel
If \(-\frac{3}{4}x + 3y - \frac{1}{2} = \frac{3}{2}y - \frac{1}{4}x\), what is the value x?


(1) \(y^2 = 4\)
(2) \(y = 2\)

\(-\frac{3}{4}x + 3y - \frac{1}{2} = \frac{3}{2}y - \frac{1}{4}x\)
--> \(-3x + 12y - 2 = 6y - x\)
--> \(2x = 6y - 2\)
--> \(x = 3y - 1\)

(1) \(y^2 = 4\)
--> \(y = ±2\)
--> x will have 2 values --> Insufficient

(2) \(y = 2\)
--> x will have only 1 value --> Sufficient

IMO Option B
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Bunuel
If \(-\frac{3}{4}x + 3y - \frac{1}{2} = \frac{3}{2}y - \frac{1}{4}x\), what is the value x?


(1) \(y^2 = 4\)

(2) \(y = 2\)

\(-\frac{3}{4}x + 3y - \frac{1}{2} = \frac{3}{2}y - \frac{1}{4}x\)
=>x=3y-1
To find the value of x, we need the value of y.

(1) \(y^2 = 4\)=> y=+2 or -2
=> x=5 or -7
From this statement we don't get a unique value of y.
Thus, insufficient.

(2) y=2
=> x=5
Thus, sufficient.

Therefore, answer is option B.
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