Knewton Brutal Math Challenge - Week 7

The "Knerd" shirts are kinda blowing up. Students at a conference last week were peaking out to them. Answer this brutal question correctly, show your work -- and it will be yours.

[pmath]a[/pmath], [pmath]b[/pmath], and [pmath]c[/pmath] are three integers such that [pmath]a[/pmath] and [pmath]b[/pmath] are less than [pmath]100[/pmath], and [pmath]c[/pmath] is less than [pmath]10[/pmath]. If [pmath]a[/pmath] and [pmath]b[/pmath] each have [pmath]2[/pmath] more distinct prime factors than [pmath]c[/pmath] has, is [pmath]ab/c[/pmath] an integer?

1) The ratio [pmath]a/b[/pmath] is greater than [pmath]1[/pmath], and when expressed as a decimal it is a terminating decimal, meaning that its decimal expression has a finite number of non-zero digits (for example, [pmath]3.4[/pmath], [pmath]2.004[/pmath], and [pmath]12[/pmath] are terminating decimals).

2) The integer [pmath]c[/pmath] is not prime.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.