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16 Sep 2014, 01:00
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If \(a\) and \(b\) are positive numbers, \(\frac{a}{b}\) is what percent of \(ab\)?
(1) \(|b - 2| = 4\)
(2) \(b^2 - 3b - 18 = 0\)
(1) \(|b - 2| = 4\)
(2) \(b^2 - 3b - 18 = 0\)
16 Sep 2014, 01:00
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Official Solution:
If \(a\) and \(b\) are positive numbers, \(\frac{a}{b}\) is what percent of \(ab\)?
Assume \(\frac{a}{b}\) is \(x\) percent of \(ab\), then:
\(ab*\frac{x}{100}=\frac{a}{b}\);
\(x = \frac{100}{b^2}\).
Hence, to answer the question we need to find the value of \(b^2\).
(1) \(|b - 2| = 4\):
\(b - 2 = 4\) or \(b - 2 = -4\);
\(b = 6\) or \(b = -2\).
Since we are told that \(b\) is positive, then \(b = 6\) and \(b^2=36\).
Sufficient.
(2) \(b^2 - 3b - 18 = 0\)
Solving gives \(b = 6\) or \(b = -3\). Since we are told that \(b\) is positive, then \(b = 6\) and \(b^2=36\).
Sufficient.
Answer: D
If \(a\) and \(b\) are positive numbers, \(\frac{a}{b}\) is what percent of \(ab\)?
Assume \(\frac{a}{b}\) is \(x\) percent of \(ab\), then:
\(ab*\frac{x}{100}=\frac{a}{b}\);
\(x = \frac{100}{b^2}\).
Hence, to answer the question we need to find the value of \(b^2\).
(1) \(|b - 2| = 4\):
\(b - 2 = 4\) or \(b - 2 = -4\);
\(b = 6\) or \(b = -2\).
Since we are told that \(b\) is positive, then \(b = 6\) and \(b^2=36\).
Sufficient.
(2) \(b^2 - 3b - 18 = 0\)
Solving gives \(b = 6\) or \(b = -3\). Since we are told that \(b\) is positive, then \(b = 6\) and \(b^2=36\).
Sufficient.
Answer: D
10 Mar 2023, 09:50
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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.
