# Solutions

Get detailed explanations to advanced GMAT questions.

### Question

**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

### Difficulty Level

Easy### Solution

Option E is the right answer.

### Option Analysis

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.**

### Related Questions

- If x/y = 2/3 , then (x-y)/x =

- (1+0.0001)/(0.04+10) The value of the expression above is closest to which of the following?

- At the end of each year, the value of a certain antique watch is “c” percent more than its value one…

- If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+1) for all positive integers…

- The logo of a certain corporation is in the shape of a polygon, where all angles of a the polygon have…