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Is m, which does not equal zero, a positive number?

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Is m, which does not equal zero, a positive number? [#permalink]

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New post 02 Feb 2016, 01:05
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Re: Is m, which does not equal zero, a positive number? [#permalink]

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New post 02 Feb 2016, 01:23
(1) m = m^2
=>m^2 - m = 0
=>m(m-1)=0
=> m = 1 , 0
m is 1 , +ve (Since m is not 0)
Sufficient
(2) m^2 = m^3
=> m^3 - m^2 = 0
=>m^2(m-1)=0
=>m= 1 , 0
m is 1 , +ve (Since m is not 0)
Sufficient
Answer D
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Re: Is m, which does not equal zero, a positive number? [#permalink]

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New post 03 Feb 2016, 00:05
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.

Is m, which does not equal zero, a positive number?

(1) m = m^2
(2) m^2 = m^3


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 m=m^2, m is not 0. Divide the equation with m and then only m=1 is derived, which is unique and sufficient.
For 2), in m^2=m^3, m is not 0. Divide the equation with m^2 and then only m=1 is derived, which is unique and sufficient. Therefore, the answer is D.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: Is m, which does not equal zero, a positive number? [#permalink]

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New post 31 Oct 2017, 04:51
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Re: Is m, which does not equal zero, a positive number?   [#permalink] 31 Oct 2017, 04:51
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