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If –9 < k < 9, is k < 0 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 50009
If –9 < k < 9, is k < 0 ?  [#permalink]

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08 Jan 2017, 07:50
00:00

Difficulty:

15% (low)

Question Stats:

82% (00:55) correct 18% (00:57) wrong based on 67 sessions

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If –9 < k < 9, is k < 0 ?

(1) 1/k < 0
(2) k^2 > 0

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Joined: 13 Apr 2010
Posts: 89
Re: If –9 < k < 9, is k < 0 ?  [#permalink]

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08 Jan 2017, 09:37
Bunuel wrote:
If –9 < k < 9, is k < 0 ?

(1) 1/k < 0
(2) k^2 > 0

From Statement 1 , 1/k < 0 => k<0
Sufficient .

Statement 2 , k^2 is always >= 0 . Ex. k = -0.5 => k^2 = 0.25 .
Not sufficient

Intern
Joined: 27 Apr 2015
Posts: 41
GMAT 1: 370 Q29 V13
Re: If –9 < k < 9, is k < 0 ?  [#permalink]

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11 Feb 2018, 02:43
Bunuel wrote:
If –9 < k < 9, is k < 0 ?

(1) 1/k < 0
(2) k^2 > 0

Stat 1 $$\frac{1}{k} < 0$$
=>Since Numerator (1 ) is +ve therefore denominator (k) has to be -ve for $$\frac{1}{k} < 0$$
=> i.e k<0 for $$\frac{1}{k} < 0$$
=> SUFFICIENT

Stat 2 $$k^2 > 0$$
=> $$k^2 > 0$$ is satisfied if k > 0 OR k < 0
=> Therefore no unique solution
=> Not SUFFICIENT

Therefore 'A'

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Dinesh
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6396
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If –9 < k < 9, is k < 0 ?  [#permalink]

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14 Feb 2018, 00:40
Bunuel wrote:
If –9 < k < 9, is k < 0 ?

(1) 1/k < 0
(2) k^2 > 0

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (k) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1):
1/k < 0 ⇔ k < 0.
The condition 1) is sufficient.

Condition 2):
k^2 > 0 ⇔ k≠0.
The condition 2) is not sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: If –9 < k < 9, is k < 0 ? &nbs [#permalink] 14 Feb 2018, 00:40
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