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20 Jun 2015, 11:58
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If \(a\) and \(b\) are single-digit positive numbers and \(\frac{a}{b}\) is NOT a recurring decimal, what is the value of \(a\)?
(1) \(-\frac{1}{3} > -\frac{a}{b} > -\frac{4}{5}\)
(2) \(b\) is equal to the sum of its positive factors, excluding \(b\) itself.
(1) \(-\frac{1}{3} > -\frac{a}{b} > -\frac{4}{5}\)
(2) \(b\) is equal to the sum of its positive factors, excluding \(b\) itself.
20 Jun 2015, 11:58
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Official Solution:
If \(a\) and \(b\) are single-digit positive numbers and \(\frac{a}{b}\) is NOT a recurring decimal, what is the value of \(a\)?
Given that \(a\) and \(b\) are single-digit positive numbers, the possible values for each are 1, 2, 3, 4, 5, 6, 7, 8, or 9.
(1) \(-\frac{1}{3} > -\frac{a}{b} > -\frac{4}{5}\)
Multiply by -1 to reverse the inequalities and simplify into: \(\frac{1}{3} < \frac{a}{b} < \frac{4}{5}\)
Convert to decimals: \(0.\overline{3} < \frac{a}{b} < 0.8\).
Since \(\frac{a}{b}\) is NOT a recurring decimal, the possible values can be 0.4 (\(a = 2\), \(b = 5\)), 0.5 (\(a = 1\), \(b = 2\)), ... Not sufficient.
(2) \(b\) is equal to the sum of its positive factors, excluding \(b\) itself.
Of the single-digit numbers, only 6 meets this condition: \(6 = 1 + 2 + 3\). Given that \(\frac{a}{b}\) is NOT a recurring decimal, then \(\frac{a}{6}\) can be either \(\frac{3}{6} = 0.5\), \(\frac{6}{6} = 1\), or \(\frac{9}{6} = 1.5\). Not sufficient.
(1)+(2) Using statement (2), we know that \(\frac{a}{b}\) can be \(\frac{3}{6} = 0.5\), \(\frac{6}{6} = 1\), or \(\frac{9}{6} = 1.5\). Among these, only 0.5 lies between \(0.\overline{3}\) and 0.8. Therefore, \(a = 3\). Sufficient.
Answer: C
If \(a\) and \(b\) are single-digit positive numbers and \(\frac{a}{b}\) is NOT a recurring decimal, what is the value of \(a\)?
Given that \(a\) and \(b\) are single-digit positive numbers, the possible values for each are 1, 2, 3, 4, 5, 6, 7, 8, or 9.
(1) \(-\frac{1}{3} > -\frac{a}{b} > -\frac{4}{5}\)
Multiply by -1 to reverse the inequalities and simplify into: \(\frac{1}{3} < \frac{a}{b} < \frac{4}{5}\)
Convert to decimals: \(0.\overline{3} < \frac{a}{b} < 0.8\).
Since \(\frac{a}{b}\) is NOT a recurring decimal, the possible values can be 0.4 (\(a = 2\), \(b = 5\)), 0.5 (\(a = 1\), \(b = 2\)), ... Not sufficient.
(2) \(b\) is equal to the sum of its positive factors, excluding \(b\) itself.
Of the single-digit numbers, only 6 meets this condition: \(6 = 1 + 2 + 3\). Given that \(\frac{a}{b}\) is NOT a recurring decimal, then \(\frac{a}{6}\) can be either \(\frac{3}{6} = 0.5\), \(\frac{6}{6} = 1\), or \(\frac{9}{6} = 1.5\). Not sufficient.
(1)+(2) Using statement (2), we know that \(\frac{a}{b}\) can be \(\frac{3}{6} = 0.5\), \(\frac{6}{6} = 1\), or \(\frac{9}{6} = 1.5\). Among these, only 0.5 lies between \(0.\overline{3}\) and 0.8. Therefore, \(a = 3\). Sufficient.
Answer: C
17 Mar 2019, 05:34
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Bunuel,
Pls explain "a/b is not a recurring decimal"
What are the chararictics of NOT RECURRING decimal.
Posted from my mobile device
Pls explain "a/b is not a recurring decimal"
What are the chararictics of NOT RECURRING decimal.
Posted from my mobile device
