Data Sufficiency

Please explain this question

20. Is 5^k less than 1,000 ?
(1) 5^k-1>3000
(2) 5^k-1=5^k-500

B

Can be answered using statement 2 alone

5^k -5^(k-1) = 500
By Law of Indices a^(m-n) = (a^m)/(a^n)

5^(k-1)(5 -1) = 500
4(5^(k-1)) = 500

Simplify to get value of k

I agree with Neo2000 that (2) is necessary and sufficient condiction to answer the quaestion. However stateembnt (1) can also provide sufficinet and necessary condiction to answer tha question because 5^(k-1) > 3000 means 5^k > 15000 > 1000, thus 5^k > 100. so the coreect answer to the quastion shoul be (D) rather than (B).

Pl. correct my understanding if found erronious.

Hi,
I agree with amitamit2020 ; Answer should be D
Otherwise, check if expressions are as written in the original question and look at the source;