If is written as the product of consecutive integers, the largest of which is 30, what is the smallest of the integers?
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Wait, is it just asking what cancels out? 30!/10! means everything from 11 to 30 stays, right? So the smallest would be 11. But that seems too easy for a GMAT question...
Yeah that's what I got too, but let me double check the wording. It says product of consecutive integers with largest being 30, so 11*12*...*30.
I think the trap is people overthinking it. The 1 through 10 cancel with part of the 30!.
This is a classic. 30!/10! = 11 x 12 x ... x 30. The consecutive integers are 11 through 30. Smallest is 11. Answer D. Easy 500 level.
Agreed, this one is pretty straightforward once you see the cancellation.
Can someone explain why it's not 1? I thought 30!/10! would leave 1 x 2 x ... x 30 divided by 1 x 2 x ... x 10, so the 1 through 10 cancel and you're left with 11 through 30. So smallest is 11.
You just answered your own question lol. Yes, 11.
I got tripped up because I was thinking about prime factorization or something. But it's literally just cancellation. The largest is 30 and they're consecutive, so the sequence is 11,12,...,30. Smallest is 11. D.
What it tests
Your understanding of divisibility rules, least common multiples, and greatest common factors.
Common trap
Forgetting that 1 is not prime and that every integer divides 0.