If n is a positive integer and k = 5.1 x 10^n , what is the value of k ?

[BTGmoderatorDC]

If n is a positive integer and k = 5.1 x 10^n , what is the value of k ?

(1) 6,000 < k < 500,000
(2) k^2 = 2.601 * 10^9


OA D

Source: Official Guide

[swerve]

If n is a positive integer and k = 5.1 x 10^n , what is the value of k ?

(1) 6,000 < k < 500,000
(2) k^2 = 2.601 * 10^9


OA D

Source: Official Guide

I guess you forget to complete the question, and I think the question is asking value of \(k\), so
\(k=5.1\cdot 10^n\)

1) Sufficient, we can easily see \(k = 51000\), and \(n = 4\). As when \(n = 3, k\) will be \(= 5.1 *\cdot 10 ^3 = 5100\), and when \(n = 5\) then \(k = 5.1 \cdot 10 ^5 = 510000\) \(\Large{\color{green}\checkmark}\)

2) Sufficient, \(k=\sqrt{2.601\cdot 10^9}\) \(\Large{\color{green}\checkmark}\)

Therefore, D

[Brent@GMATPrepNow]

If n is a positive integer and k = 5.1 x 10^n , what is the value of k ?

(1) 6,000 < k < 500,000
(2) k^2 = 2.601 * 10^9


OA D

Source: Official Guide

Target question: What is the value of k?

Given: n is a positive integer, and k = (5.1)x(10^n)
IMPORTANT: This since n can be ANY positive integer, there are several possible values of k.
They are: 51, 510, 5100, 51000, 510000, etc

Statement 1: 6,000 < k < 500,000
If we examine the possible values of k (51, 510, 5100, 51000, 510000, etc ), we can see that only ONE value (51,000) lies within the range defined by the inequality.
So, k must equal 51,000
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: k² = 2.601 x 10^9
If k²= 2.601 x 10^9, then EITHER k = √(2.601 x 10^9) OR k = -√(2.601 x 10^9). So, it appears that we cannot answer the target question.
HOWEVER, the question also tells us that k = 5.1 x 10^n, and since 5.1 x 10^n will always have a POSITIVE value, we know that k must be POSITIVE.
If k is POSITIVE, then k ≠ -√(2.601 x 10^9)
This means that k must equal √(2.601 x 10^9)
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent