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 Author: Bunuel [ 13 Mar 2020, 05:33 ] Post subject: Does positive integer b have a factor n such that 1 < n < b ? 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.

 Author: GMATWhizTeam [ 13 Mar 2020, 06:04 ] Post subject: Re: Does positive integer b have a factor n such that 1 < n < b ? Bunuel wrote: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 statementsStatement 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.

 Author: bumpbot [ 22 Nov 2022, 11:41 ] Post subject: Re: Does positive integer b have a factor n such that 1 < n < b ? Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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