Bunuel
Does positive integer b have a factor n such that 1 < n < b ?
(1) b = 2k, where k is an integer greater than 1.
(2) k is a factor of b, where k is an integer greater than 1.
Step 1: Analyze Question Stem
• We need to find out if the positive integer b has a factor n that lie between 1 and b.
• Now, there can be two scenarios:
o Case 1: b has a factor that lies between 1 and b. This would mean that b is a composite number. For example: If b= 6 then b has factors 2 and 3 between 1 and 6.
o Case 2: b does not have a factor between 1 and b. This would mean that b is a prime number. For example: b = 5 does not have any factor between 1 and 5.
So, the question is indirectly asking us to find out,
if b is a composite number or a prime number?
Step 2: Analyze individual statements
Statement 1: b = 2k, where k is an integer greater than 1.
• If k is an integer greater than 1.
o Then b is an even number greater than 2.
Which means b is definitely a composite number.
Hence, statement 1 is sufficient and we can eliminate answer options B, C, and E.
Statement 2: k is a factor of b, where k is an integer greater than 1.
• If k is factor of b and k is an integer, greater than 1, then there can be 2 possibilities.
o Case 1: Say b = 6
Then k can be 2 or 3 or 6 and b is a composite number.
o Case 2: Say b = 5
Then k will be equal to 5 and b is a prime number.
Since, we are getting two different answers, statement 2 is not sufficient and the correct answer is
Option A.