What is the Value of k^2 - k? GMAT Data Sufficiency

Question: What is the value of k^2 - k?

(1) The value of k - 1/k is 1.
(2) The value of 2k –1 is √5

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

“What is the value of k^2 - k?” – 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 sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

In this question, it has asked to find out the value of k^2 - k

1. (k-1) / k = 1

Rearrange to have k-1 = k

Factor original equation to k(k-1)
Substitute k with k -1 to get (k-1)(k-1) = 0
k =1, sufficient

2. Solve for k

k = (sqrt(5) + 1)/2
There is no need to solve it, as it will be a value that you plug into the original equation. Sufficient
sqrt(5) will be a positive number as it's an even root, so no need to worry about a negative value

Hence, D is the correct answer.

Correct Answer: D

Approach Solution 2:

In this question, it has asked to find out the value of k^2 - k
Original Statement is K^2 - K =?
K(K-1) = ?

Statement 1:
k- (1/K) = 1
(K^2 -1) / K = 1
K^2 = K +1
Putting Value of K^2 in original, we will get answer ---- Statement 1 Sufficient

Statement 2:
2K - 1 = sqrt(5)
Statement 2 is sufficient to find the unique value of K and hence can answer the original Statement.

Answer: Each one is sufficient - Option D is the correct choice.

Correct Answer: D

Approach Solution 3:

In this question, it has asked to find out the value of k^2 - k
here we need the value of k^2-k

Statement 1 gives
K-1 / k = 1
k^2 - 1 = k
k^ -k = 1

Hence, it is sufficient to get the answer.

Statement 2 gives
here we have k
so we can get k ^ 2
so we can get k^2 - k

Hence, it is sufficient to get the answer.

Correct Answer: D

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