DS Question - 26

Is 5^k less than 1,000?

(1) 5^(k-1) greater than 3,000

(2) 5^(k-1) = 5^k - 500


Answer: D

From statement (1) - 5^(k-1) is greater than 3000

=> 5^k/5 is greater than 3000
=> 5^k is greater than 15000

Hence sufficient

From statement (2) - 5^(k-1) = 5^k - 500

=> 5^(k-1) = 5^k - 500
=> 5^k - 5^(k-1) = 500
=> 5^k(1- 5^-1) = 500
=> 5^k(4/5) = 500
=> 5^k = 2500/4 = 625
Therefore 5^k is less than 1000

Hence sufficient