Hi I am reviewing my questions from my PSAT to prepare for the SAT in Fall. The question is if n/6 is a positive integer, which of the following must be a factor of n?
a) 3
b) 4
c) 5
d) 7
e) 11
A is the correct answer which I understand because 3 is a factor of 6 (3*2) and 6/6 gives us the positive integer of 1 but wouldn't b work too? Because 4 is a factor of 12 (4*3) and 12/6 gives us a positive integer of 2. Please help. Thanks :)

Question

Hi I am reviewing my questions from my PSAT to prepare for the SAT in Fall. The question is if n/6 is a positive integer, which of the following must be a factor of n?
a) 3
b) 4
c) 5
d) 7
e) 11
A is the correct answer which I understand because 3 is a factor of 6 (3*2) and 6/6 gives us the positive integer of 1 but wouldn't b work too? Because 4 is a factor of 12 (4*3) and 12/6 gives us a positive integer of 2. Please help. Thanks :)

anonymous · Answer

3 must be the answer since for any positive integer n such that n/6 is still a positive integer (which implies n/6 is divisible by 6, hence also divisible by 3), n will always be divisible by 3. because if we choose 4, for some integers n, the conditions above may not hold. if you have n=6, clearly n/6 is positive integer and it has factor of 3 but not 4.

anonymous · Answer

the word "must" means it must apply for any positive integer n divisible by 6. If it said could be a factor, then all the answers are correct (i.e. the positive numbers 4*6, 5*6,7*6,11*6)

anonymous · Answer

Okay wait I think I got it...so if we choose 4 as an answer then 8 might be true since 4 goes into 8 but it can't be divisble by 6. gotcha...

anonymous · Answer

Yes. In addition, integers are numbers that are even like whole numbers. Most multiples of 3 can divide 6. Well, more than half anyway.

anonymous · Answer

Okay...:)