Is n/18 an integer? (1) 5n/18 is an integer. (2) 3n/18 is

[Kapil_Tundwal]

Q. Is n/18 an integer?

(1) 5n/18 is an integer.
(2) 3n/18 is an integer.

Explanation suggests 1 is insufficient. Explanation conviniently takes following 2 cases to illustrate that is insufficient.

(1) INSUFFICIENT: We are told that 5n/18 is an integer. This does not allow us to determine whether n/18 is an integer. We can come up with one example where 5n/18 is an integer and where n/18 is NOT an integer. We can come up with another example where 5n/18 is an integer and where n/18 IS an integer.

Let's first look at an example where 5n/18 is equal to the integer 1.

If 5n/18 = 1, then n/18 = 1/5 -> In this case n/18 is NOT an integer.

Let's next look at an example where 5n/18 is equal to the integer 15.

If 5n/18 = 15, then n/18 = 3 -> In this case n/18 IS an integer.

Thus, Statement (1) is NOT sufficient.

As I see it if 5n/18 is an integer, it has to be that 18 is a factor of n, since 5 cannot further divide 18. Hence this should be sufficient - whats wrong with explanation?

[StaceyKoprince]

Your logic would be right if n were required to be an integer - but no such constraint is given in the problem. If n is a fraction, then just the numerator of that fraction would have to include the 18 necessary to make 5n/18 an integer.

For example, if n = 18/5
then 5n/18 = 5(18/5) = 18, which is an integer
BUT n/18 = (18/5)/18 = 1/5, which is not an integer