Data Sufficiency

theachiever wrote:Is 5^k less than 1000?

1)5^k+1>3000
2)5^k-1=5^k-500

I tried the following approach.Experts ,kindly let me know if this is correct
I got the answer to be D but the OA given is B.

My Approach.
1.If 5^k+1 has to be greater than 3000 then the least value of k should be atleast 4 since 5^5=3125>3000 and hence 5^4 <1000 from A

2.Using the statement 2 I tried random values for k which did not satisfy this condition except k=4
in which case again we can determine if 5^k <1000


Kindly explain.

Do not overly restrict the problem.
The value of k does not have to be an integer.

Statement 1: 5^(k+1) > 3000
Since (5^k)(5^1) = 5^(k+1), we get:
(5^k)(5^1) > 3000
5^k > 600.
If 5^k = 700, then 5^k < 1000.
If 5^k = 2000, then 5^k > 1000.
INSUFFICIENT.

Statement 2: 5^(k-1) = 5^k - 500
Whereas statement 1 is an INEQUALITY, statement 2 is an EQUATION.
Since the value of k can be determined from this equation, SUFFICIENT.

The correct answer is B.

Here's the algebra for statement 2:
5^(k-1) = 5^k - 500
5^k - 5^(k-1) = 500.

Since (5^k)(5^-1) = 5^(k-1), we get:
5^k- (5^k)(5^-1) = 500

5^k - (5^k)(1/5) = 500.

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

(5^k)(4/5) = 500

5^k = 625.