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# Is 13N a positive number?

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
Is 13N a positive number?  [#permalink]

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17 Mar 2016, 23:21
00:00

Difficulty:

15% (low)

Question Stats:

76% (00:58) correct 24% (01:18) wrong based on 185 sessions

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Is 13N a positive number?

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

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Re: Is 13N a positive number?  [#permalink]

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18 Mar 2016, 12:37
St1: -ve * +ve = -ve. So N is positive. Sufficient

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

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Re: Is 13N a positive number?  [#permalink]

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19 Mar 2016, 01:05
Bunuel wrote:
Is 13N a positive number?

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

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

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Re: Is 13N a positive number?  [#permalink]

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19 Mar 2016, 22:22
1
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.

 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 13N a positive number?  [#permalink]

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18 Apr 2017, 15:35
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Top Contributor
Bunuel wrote:
Is 13N a positive number?

(1) -21N is a negative number
(2) N² < 1

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

Cheers,
Brent
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Re: Is 13N a positive number?  [#permalink]

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08 Feb 2019, 22:36
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Re: Is 13N a positive number?   [#permalink] 08 Feb 2019, 22:36
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