Is n/18 an integer?

[jeffwey]

statement 1 alone:
if 5n/18 = 5, then n = 18, for which n/18 is an integer; if 5n/18 = 1, then n = 18/5, which is not an integer (and so therefore n/18 isn't an integer either). insufficient.
note that we are picking values for 5n/18, NOT values for n - per the problem statement!

statement 2 alone: reduce 3n/18 to n/6 to make this statement easier to think about.
if n/6 = 3, then n = 18, for which n/18 is an integer; if n/6 = 1, then n = 6, for which n/18 is not an integer. insufficient.
note that we are picking values for 3n/18, NOT values for n - per the problem statement!)

together:
remember that sums and differences of integers are also integers.
if 5n/18 and 3n/18 are integers, then 5n/18 - 3n/18 = 2n/18 is also an integer. once we have that, 3n/18 - 2n/18 = n/18 is also an integer. sufficient.

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if the problem had stated that n must be an integer, then statement (1) would become sufficient, but statement (2) would still be insufficient.

[jlucero]

That's the big trick on this one, Jeff. Good explanation.