Baten80 wrote:

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

(1) 6,000 < k < 500,000

(2) k^2 = 2.601 * 10^9

I understand the official explanation. is there any other easy way?

Question should read:

If n is a positive integer and k = 5.1 * 10^n, what is the value of k ?As n is a positive integer then k could be: 51, 510, 5,100, 51,000, ... Also note that no matter the value of n, k is always a positive number.

(1) 6,000 < k < 500,000 --> only one number from above is in this range: 51,000. Sufficient.

(2) k^2 = 2.601 * 10^9 --> we can solve quadratics to get two values of k positive and negative, but since given that k is positive then only the positive value of k will be valid. Sufficient.

Answer: D.