If k is a positive integer, then 20k is divisible by how many different positive integers?
(1) k is prime
(2) k = 7
(1) k is prime
(2) k = 7
[Reveal] Spoiler:
Divisible by a positive integer -> factor
No of factors for a number in the form (a^x)(b^y)(c^z) is given by (x+1)(y+1)(z+1)
20k = (2^2)(5^1)(k)
Stmt 1 says k is prime. so 20k = (2^2)(5^1)(k^1). Total # of factors is (2+1)(1+1)(1+1). So sufficient.
Stmy 2 says k = 7 so again Total # of factors is (2+1)(1+1)(1+1). So sufficient.
Hence answer is D, but that is not the OA. What am I missing?
No of factors for a number in the form (a^x)(b^y)(c^z) is given by (x+1)(y+1)(z+1)
20k = (2^2)(5^1)(k)
Stmt 1 says k is prime. so 20k = (2^2)(5^1)(k^1). Total # of factors is (2+1)(1+1)(1+1). So sufficient.
Stmy 2 says k = 7 so again Total # of factors is (2+1)(1+1)(1+1). So sufficient.
Hence answer is D, but that is not the OA. What am I missing?