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If m is a positive integer, is √13m an integer? 1) 117m i

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If m is a positive integer, is √13m an integer? 1) 117m i

by Max@Math Revolution » Mon Mar 21, 2016 5:32 pm
If m is a positive integer, is √13m an integer?

1) 117m is the square of an integer.
2) m/117 is the square of an integer.


* A solution will be posted in two days.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu Mar 24, 2016 3:56 pm
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If m is a positive integer, is √13m an integer?

1) 117m is the square of an integer.
2) m/117 is the square of an integer.


In the original condition, there is 1 variable(m), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), in order to satisfy 117m=3^213m=integer^2, m should be 13t^2(t=some integer). √13m=√(〖13^〗^2 〖t^〗^2 )=13t is derived, which is yes and sufficient.
For 2), from m/117=integer^2, m=117integer^2=3^213n^2 (n=some integer) is derived. When substituting m, √13m=√(〖13^〗^2 3^(^2) 〖n^〗^2 )=13(3)n is derived, which is yes and sufficient.
Thus, D is the answer.
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