Question: If k is not equal to 0, 1, or -1 is 1/k>0?

1. 1/k−1>0
2. 1/k+1>0

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“If k is not equal to 0, 1, or -1 is 1/k>0?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:
Approach Solution 1:
If k#0, 1 or -1 is 1/k>0?

Basically the question asks: is k>0?

(1) 1/k−1>0 --> denominator is positive: k−1>0--> k>1, hence 1/k>0. Sufficient.
(2) 1/k+1>0--> denominator is positive: k+1>0 → k>−1, hence k can be negative as well as positive: 1/k may or may not be >0. Not sufficient.

Correct Answer: A

Approach Solution 2:
(1)k−1 is positive. So k must be greater than 1,
Actually, k−1>0, k>1, So; 1/k>0. Sufficient.

(1) k+1 is positive, but k can be a negative fraction such as -0.5 is k+1>0, k can be 2. Actually, k+1>0, or k>−1;

So; 1/k>0 can be Negative or Positive.
Insufficient.

Correct Answer: A

Approach Solution 3:
Let us take statement I - In this, it is given that 1/(k-1) >0. This implies that k must be positive and k must be greater than 1. Hence, 1/k is definitely greater than zero. For example, k's value is 2, then 1/(2-1) = 1 which is > 0. This implies that 1/2 = 0.5 which is still greater than '0'. Hence, this is sufficient.

Let us take II - It says 1/ (k+1) > 0 which means that this will satisfy both positive and negative values of k which are less than -1. For example, if k is 2, 1/(k+1) is >0 and 1/k wll be >0. But if k's value is -0.5, it will satisfy the second equation but 1/k will be -2 which is <0 and hence, INSUFFICIENT.

Correct Answer: A

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