official guide - DS # 125

[freedsl]

If r and s are positive integrers, is r/s an integer?

1) every factor of s is also a factor of R.
2) every prime factor of s also a prime factor of r.


The answer is A but I don't get it, shouldn't it be E. if (1) states every factor of s is also a factor of r, it could be that s has two factors of 3 but r has only one factor of 3 and at the end, we get one factor of 3 left for 4 and we don;t get an integer. the explanation in the book makes no sense to me. I have the 11th edition.

IF they has used the word "All" rather than "every", it would make better sense to me.

help please

Thanks

[netigen]

we have to find if R/S = integer

if S is a factor of R then R/S = integer

(A) states that every factor of S (which includes S itself) is a factor R hence R/S = integer
(B) states that every PRIME factor of S (which may or may not include S) is a factor of R hence R/S may or may not be integer

hence only A solves the problem for us

[freedsl]

we have to find if R/S = integer

if S is a factor of R then R/S = integer

(A) states that every factor of S (which includes S itself) is a factor R hence R/S = integer

so lets say that every factor of s is also a factor of R, lets say the factors of s are 2.3.3.5.7 and r is 2.3.5.7, so we have every factor of s be a factor of R but R/S is not an integer.

What is it that I'm missing, particulary I don't the assumption that "if S is a factor of R then R/S"?? how do you make this assumption from the question stem and part (1).

is it becasue "everyfactor" includes s itself so that my example with the extra 3 is not a valid case??

thanks

[freedsl]

I guess i answerd my own question, thanks for your note