The function for an integer is defined by the number of prime factors of . What is the value of ?
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I got stuck because I wasn't sure if f(n) counts distinct prime factors or total with multiplicity. The wording 'number of prime factors' is ambiguous. Can someone clarify?
I think in most GMAT problems, unless specified, 'prime factors' means distinct. But here, if you factor 210 and 143, you get multiple primes. Let's see what others say.
Actually, the function is defined as the number of prime factors of n. Typically, that means the count of distinct primes. But if it's total, the answer might differ. We need to be careful.
This was tricky but doable. First I factored 210 = 2*3*5*7, and 143 = 11*13. So 210*143 has 6 distinct prime factors. Then f(210*143) = 6. Then f(6) = 2 because 6 = 2*3. So answer is 2. But wait, is 6 considered to have 2 prime factors? Yes. So I think B is correct.
Nice breakdown! I initially thought f(6) might be 1 if they only count distinct, but 6 has two distinct primes. So 2 makes sense.
I'm confused about whether f(n) counts prime factors with multiplicity. For example, if n=12, would f(12) be 3 (2,2,3) or 2 (2,3)? The problem doesn't specify. In many contexts, it's the number of distinct prime factors. But I've seen some problems where it's the total number. Need clarity.
What it tests
Your ability to evaluate and compose functions, including unusual defined operations.
Common trap
Applying function operations in the wrong order or ignoring domain restrictions.