That's a great approach, Govi.
We can also solve by considering prime factors.
Is x divisible by 15?
Well, if x were divisible by 15, then x would contain 3 and 5 in its prime factorization.
(1) tells us that x is a multiple of 10. This means x contains 5 in its prime factorization. But we don't know if it has 3. Insufficient.
(2) tells us that x^2 is a multiple of 30. Now, if we knew that x were an integer, then this would mean that x contains 2, 3 and 5 in its prime factorization, and (2) would be sufficient. But as gmatmachoman rightly points out x may easily be a non-integer, such as sqrt 30.
Insufficient.
From (1) we know that x is divisible by 10--thus, x is an integer....choose C.
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For these number property DS questions, if the theory/concepts jump out at you, then solve that way. If not, then pick numbers. But quite often you can pick numbers and use/discover a bit of theory at the same time. In yes/no questions, through picking numbers, you can prove insufficiency by getting different answers (yes vs no). While you can't prove sufficiency, if you keep getting "yes" or keep getting "no" using different kinds of numbers, then you can convince yourself of sufficiency.
Kaplan Teacher in Toronto
