GMAT Data Sufficiency- Given k is a Nonzero Integer, is k>0?

Question: Given k is a nonzero integer, is k>0?

(1) |k−4|=|k| + 4
(2) k>k^3

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

“Given k is a nonzero integer, is k>0?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". 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 sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

Given to us that k is a non-zero integer. It is asked if k > 0 or not.
There are two statements, we have to check whether these two statements are sufficient to answer the problem or not.
Coming to the first statement,
1)|k-4| = |k| + 4
In order to remove the mod we have to break the values of k into different regions.
We’ll break the values of k where the mod values become 0.
|k-4| = 0
k = 4
also,
|k| = 0
k = 0
Therefore we’ll break the values into three different regions
K <= 0 , 0 < k < 4 and k >= 4
So for k <= 0
Given equation becomes,
| k-4 | = | k| + 4
-(k-4) = - k + 4
- k + 4 = -k + 4
As we get 0 = 0 the value of k cannot be found but the equation is satisfied.
Therefore k < 0
for the second case,
0 < k < 4
| k-4 | = | k| + 4
-(k-4) = k + 4
-k+4 = k + 4
2k = 0
k=0
But we assumed k > 0
Therefore k cannot be in the region 0 < k< 4
For case 3,
K >= 4
| k-4 | = | k| + 4
k-4 = k+ 4
We get 8 = 0
Therefore k cannot be greater than 4.
Finally, we get k <0. Therefore this statement is sufficient to get the answer.
Coming to the second statement,
K > k^3
On the number line, it should be noted that the value of x > x^3 only when x < -1 or 0 < x < 1
But in the given question, it is given that k is an integer. Therefore it will not lie in the region 0 < x < 1 Therefore k must be less than -1.
We can say that k < 0 . Therefore this statement is sufficient to answer the question.

Correct Answer: D

Approach Solution 2:

Assumed to be a non-zero integer, k. If k > 0 or not is the question.
There are two assertions, and we must determine if they are adequate to address the issue.
When it comes to the first claim,
1)|k-4| = |k| + 4
We must divide the values of k into several areas in order to eliminate the mod.
Where the mod values become 0, we will divide the values of k.
k = 4 and |k-4| = 0.
|k| = 0\sk = 0
As a result, we'll divide the data into three zones.
K = 0, K >= 4, and K = 0
Thus, if k = 0,
As a result of the above equation, | k-4 | = | k| + 4 -(k-4) = - k + 4 - k + 4 = -k + 4
The value of k cannot be obtained since we arrive to 0 = 0, but the equation is still fulfilled.
For the second example, k 0 because 0 k 4 | k-4 | = | k| + 4 -(k-4) = k + 4 -k+4 = k + 4 2k = 0 k=0
However, we figured k > 0
Consequently, k cannot exist in the range 0 k 4.
In the third scenario, K >= 4 | k-4 | = | k| + 4 k-4 = k+ 4
However, it is stated in the question that k is an integer. Therefore, it won't be in the area 0 x 1. k must thus be smaller than -1.
K 0, as we can see. As a result, this assertion provides a complete response to the question.
We get 8 = 0
K can't thus be bigger than 4.
We finally get to k 0. Consequently, this claim is adequate to elicit the response.
K > k3 refers to the second claim.
It should be noticed that on the number line, the value of x > x3 only occurs when x -1 or 0 x 1.

Correct Answer: D

Approach Solution 3:

k is considered to be a positive integer. The question is whether k > 0 or not.
We must evaluate whether the two claims are sufficient to solve the issue.
Regarding the first claim, 1)|k-4| = |k| + 4
To get rid of the mod, we must split up the k values into several regions.
We will split the k values when the mod values become 0.
k = 4 and |k-4| = 0.
|k| = 0\sk = 0
In order to do this, we'll split the data into three zones.
K >= 4, K 0, and K 0.
As a result, k = 0
The equation above gives the following results: | k-4 | = | k| + 4 -(k-4) = - k + 4 - k + 4 = -k + 4.
Since we get to 0 = 0, we cannot determine the value of k, but the equation is still true.
In the second instance, k 0 is obtained because 0 k 4 | k-4 | = | k| + 4 -(k-4) = k + 4 -k+4 = k + 4 2k = 0 k=0.
But we concluded that k > 0.
Therefore, k cannot occur in the interval 0 k 4.
K >= 4 | k-4 | = | k| + 4 k-4 = k+ 4 in the third case.
However, the question clearly says that k is an integer. As a result, it won't be in the region 0 x 1. K 0, as we can see, means that k must be less than -1. As a consequence, this claim offers a comprehensive answer to the query.
Since we obtain 8 = 0, K cannot be more than 4.
Finally, we reach k 0. As a result, this argument can generate the desired response.
K > k3 alludes to the second statement.
On the number line, it should be noted that the value of x > x3 only appears when x -1 or 0 x 1.

Correct Answer: D

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GMAT Data Sufficiency- Given k is a Nonzero Integer, is k>0?

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