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26 May 2017, 04:42
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If \(m\), \(n\), and \(p\) are positive integers, \(mnp=\)?
(1) \(m^{4}np = 2,835\)
(2) \(p = 7\)
(1) \(m^{4}np = 2,835\)
(2) \(p = 7\)
26 May 2017, 04:42
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Official Solution:
In the original condition, there are 3 variables \((m, n, p)\). In order to match the number of variables to the number of equations, there must be 3 equations. Therefore, E is most likely to be the answer.
By solving con 1) & con 2), you might get \(2,385 = (3^{4})(5)(7)\), but if you find the "hidden 1" (you can put 1 into the multiplication because 1 is also positive integer) in \(6 = (2)(3) = (1)(6), 2,385 = (3^{4})(5)(7) = (1^{4})(405)(7)\) is also possible. So, from \(mnp=(3)(5)(7), (1)(405)(7)\), the answers are not unique, hence it is not sufficient. Therefore, the answer is E.
Answer: E
In the original condition, there are 3 variables \((m, n, p)\). In order to match the number of variables to the number of equations, there must be 3 equations. Therefore, E is most likely to be the answer.
By solving con 1) & con 2), you might get \(2,385 = (3^{4})(5)(7)\), but if you find the "hidden 1" (you can put 1 into the multiplication because 1 is also positive integer) in \(6 = (2)(3) = (1)(6), 2,385 = (3^{4})(5)(7) = (1^{4})(405)(7)\) is also possible. So, from \(mnp=(3)(5)(7), (1)(405)(7)\), the answers are not unique, hence it is not sufficient. Therefore, the answer is E.
Answer: E
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