Get detailed explanations to advanced GMAT questions.

**Which of the following is an integer?**

**I. 12! / 6! II. 12! / 8! III. 12! / 7!5!**

Option A:

I only

Option B:

II only

Option C:

III only

Option D:

I and II only

Option E:

I, II, and III

Option E is the right answer.

12!/6! = 12*11*10*9*8*7*6!/6! = Integer.

12!/8! = 12*11*10*9*8!/8! = Integer.

12!/7!*5! = 12*11*10*9*8/5*4*3*2*1 = integer

All 3 options finally yield an integer.

**So, the answer is E.**

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