If k is a positive integer, then 20k is divisible by how many different positive integers?
1. k is prime
2. k is 7
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?
What you are missing in F.S 1, is that we don't know the value of k.
Scenario I: k=2, the total no of factors for 20k = \(2^2*5*2 = 2^3*5 = (3+1)*(1+1) = 8\)
Scenario II: k=3, the total no of factors for 20k = \(2^2*5*3 = (2+1)*(1+1)*(1+1) = 12.\)
Hence, 2 different answers, thus, Insufficient.
All that is equal and not-Deep Dive In-equality
Hit and Trial for Integral Solutions