How many of the factors of 210 are odd numbers greater than 1?
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Wait, is the trick here to only look at the odd prime factors? Because 210 = 2 × 3 × 5 × 7, and the 2 is just going to make even copies of every odd factor. So counting odd divisors > 1 should just be subsets of {3,5,7}. Is that the intended shortcut?
Yes exactly, the 2 doesn't affect the odd part at all, so ignore it.
That was my approach too, way faster than listing everything.
I initially just listed all factors of 210 and then filtered the odd ones, but I definitely missed one on the first pass. Gotta be careful with 1, it's odd but excluded by the 'greater than 1' part.
Same trap here. I counted 1 and got the wrong choice.
Took me a minute to see why the answer isn't just the number of odd prime factors. The phrasing 'factors of 210' includes products like 15, 21, 35, not just the primes themselves.
Right, that's the key distinction. Subsets include combinations.
This is exactly where I slipped on my first attempt.
Solid 655-705 level question. Not insanely hard but enough little traps (1, the even factor 2, combinations of odds) to punish rushing.
What it tests
Your command of divisibility, primes, factors, parity, and how the GMAT tests properties of integers.
Common trap
Forgetting that 1 is not prime, that 0 is divisible by every integer, or that negative numbers flip your assumptions.