If –9

Question

If –9 < k < 9, is k < 0 ?

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

sb0541 · Answer

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 Answer is A .

dineshril · Answer

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' Regards Dinesh

MathRevolution · Answer

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.

Therefore, the answer is A.

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.

If –9 < k < 9, is k < 0 ?

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GMAT Data Sufficiency (DS) Questions

If –9 < k < 9, is k < 0 ?

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