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GMAT Inequalities is a high-frequency topic in GMAT Quant, but many students struggle because the concepts behave differently from standard algebra. Understanding the right rules, patterns, and edge cases can significantly improve both speed and accuracy.- May 06
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16 Sep 2014, 00:14
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If \(x\) is a positive number and \(\frac{1}{2}*\sqrt{x} = 2x\), what is the value of \(x\)?
A. \(0\)
B. \(\frac{1}{16}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{2}\)
E. \(1\)
A. \(0\)
B. \(\frac{1}{16}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{2}\)
E. \(1\)
16 Sep 2014, 00:14
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Official Solution:
If \(x\) is a positive number and \(\frac{1}{2}*\sqrt{x} = 2x\), what is the value of \(x\)?
A. \(0\)
B. \(\frac{1}{16}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{2}\)
E. \(1\)
Cross-multiply: \(\sqrt{x} = 4x\)
Square both sides of the equation to eliminate the square root: \(x = 16x^2\)
Given that \(x\) is a positive number, we can safely divide both sides by \(x\): \(1 = 16x\). This gives us \(x = \frac{1}{16}\).
Answer: B
If \(x\) is a positive number and \(\frac{1}{2}*\sqrt{x} = 2x\), what is the value of \(x\)?
A. \(0\)
B. \(\frac{1}{16}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{2}\)
E. \(1\)
Cross-multiply: \(\sqrt{x} = 4x\)
Square both sides of the equation to eliminate the square root: \(x = 16x^2\)
Given that \(x\) is a positive number, we can safely divide both sides by \(x\): \(1 = 16x\). This gives us \(x = \frac{1}{16}\).
Answer: B
07 May 2023, 14:19
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
