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87% (01:30) correct
13%
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If -3/4*x+3y-1/2=3/2*y-1/4*x what is the value of x?
(1) y^2=4
(2) y=2
Quant_3q.JPG [ 6.08 KiB | Viewed 5119 times ]
(1) y^2=4
(2) y=2
Attachment:
Quant_3q.JPG [ 6.08 KiB | Viewed 5119 times ]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
28 Jan 2011, 06:11
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If -3/4*x+3y-1/2=3/2*y-1/4*x what is the value of x?
\(-\frac{3}{4}*x+3y-\frac{1}{2}=\frac{3}{2}*y-\frac{1}{4}*x\) --> \(\frac{3}{2}*y-\frac{1}{2}=\frac{1}{2}x\) --> \(x=3y-1\).
(1) y^2=4 --> \(y=2\) or \(y=-2\) --> \(x=5\) or \(x=-7\). We have two values of \(x\), hence this statement is not sufficient.
(2) y=2 --> \(x=5\). Sufficient.
Answer: B.
As for your question: \(x^2=4\) means that \(x=2\) or \(x=-2\), as both values satisfy \(x^2=4\): \((-2)^2=4\) as well as \(2^2=4\). In contrast, the equation \(x=\sqrt{4}\) has one solution: \(x=2\) (that's because square root function can not give negative result: wich means that \(\sqrt{some \ expression}\geq{0}\), or \(\sqrt{x}\geq{0}\). So, when the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the non-negative root).
Hope it's clear.
\(-\frac{3}{4}*x+3y-\frac{1}{2}=\frac{3}{2}*y-\frac{1}{4}*x\) --> \(\frac{3}{2}*y-\frac{1}{2}=\frac{1}{2}x\) --> \(x=3y-1\).
(1) y^2=4 --> \(y=2\) or \(y=-2\) --> \(x=5\) or \(x=-7\). We have two values of \(x\), hence this statement is not sufficient.
(2) y=2 --> \(x=5\). Sufficient.
Answer: B.
As for your question: \(x^2=4\) means that \(x=2\) or \(x=-2\), as both values satisfy \(x^2=4\): \((-2)^2=4\) as well as \(2^2=4\). In contrast, the equation \(x=\sqrt{4}\) has one solution: \(x=2\) (that's because square root function can not give negative result: wich means that \(\sqrt{some \ expression}\geq{0}\), or \(\sqrt{x}\geq{0}\). So, when the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the non-negative root).
Hope it's clear.
