St1: -ve * +ve = -ve. So N is positive. Sufficient

St2: -1 < N < 1. N can be positive or negative. Not sufficient

Answer: A

1) -21 N = -ve .. so N is clear +.......Suff

2) (1/2) ^2 & (-1/2)^2 is less than one So N could either -ve or +ve.........Insuff

Answer: A

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 13N a positive number?

(1) -21N is a negative number
(2) N^2 < 1


When you modify the original condition and the question, 13n>0? becomes n>0?. There are 1 variables(n), 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), divide -21n<0 with -21 and n>0 is yes, which is sufficient.
For 2), from -1<n<1, n=-0.1 is no but n=0.1 is yes, which is not sufficient.
Therefore, the answer is A.


 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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Target question: Is 13N a positive number?

Statement 1: -21N is a negative number
We know that (NEGATIVE)(POSITIVE) = NEGATIVE
Since -21 is NEGATIVE, it must be the case that N is POSITIVE
If N is POSITIVE, then 13N is definitely a positive number
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: N² < 1
There are several values of N that satisfy statement 2. Here are two:
Case a: N = 1/2, in which case N² = (1/2)² = 1/4, which is less than 1. In this case 13N = (13)(1/2) = 6.5. So, 13N is POSITIVE
Case b: N = -1/2, in which case N² = (-1/2)² = 1/4, which is less than 1. In this case 13N = (13)(-1/2) = -6.5. So, 13N is NEGATIVE
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

Cheers,
Brent
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