Number Systems -Sequence and Series

sukhman wrote:In a certain sequence, term(n) = (2n)! ÷ n! is defined for all positive integer values of n. If x is defined as the product of the first 10 ten terms of this sequence, which of the following is the greatest factor of x?
(A) 220
(B) 230
(C) 245
(D) 252
(E) 255

The wording in the original post is a little off. We don't typically refer to f(n) as a sequence. I have reworded the question so that it's more GMAT-like.

Let's take a look at a couple of terms in this sequence.
term(n) = (2n)! ÷ n!
So, term1 = 2! ÷ 1! = (2)(1)/(1) = 2
- term2 = 4! ÷ 2! = (4)(3)(2)(1)/(2)(1) = (4)(3)
- term3 = 6! ÷ 3! = (6)(5)(4)(3)(2)(1)/(3)(2)(1) = (6)(5)(4)
- term4 = 8! ÷ 4! = (8)(7)(6)(5)(4)(3)(2)(1)/(4)(3)(2)(1) = (8)(7)(6)(5)
.
.
.
term10 = 20! ÷ 10! = (20)(19)(18)(17)(16)(15)(14)(13)(12)(11)

So, x = the product of all of the blue numbers.

Which of the following is the greatest factor of x?
Let's start with the largest number among the answer choices.

E) 255
255 = (3)(5)(17)
IMPORTANT: Notice that, among the blue numbers in the product x, there is a 3, a 5 and a 17.
This means that 255 is, indeed, a factor of x.
Since 255 is the biggest of the five answer choices, the correct answer is E

Cheers,
Brent