DS Question - 25

Is 5^k less than 1,000?

(1) 5^(k-1) is less than 3000
(2) 5^(k-1) = 5^k - 500

Answer: B

From statement (1) - It is given that 5^(k-1) less than 3000
=> 5^k/5 less than 3000
=> 5^k less than 15000
=> 5^k could be either more than 1,000 or less than 1,000.
Hence insufficient

From statement (2) - It is given that 5^(k-1) = 5^k - 500
=> 5^k/5 = (5^k) - 500
=> 5^k = 5*(5^k) - 2500
=> (5-1)*5^k = 2500
=> 4*5^k = 2500
=> 5^k = 2500/4 = 625

Hence 5^k less than 1,000.

Hence sufficient.