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It’s Not An Excited Number; It’s a Factorial!

If you’ve ever come across a number with an exclamation mark in front of it, that’s the factorial sign, e.g. 5!.

Factorials don’t come up too often on the GRE, and when they do, it’s usually on harder problems. Still, you don’t want to be faced with an exclamation sign next to a number and then exclaim yourself, “What in the world!” (For the more expletive prone you can use your imagination!)

But no need to worry—just think of the factorial sign as a countdown. Whichever number is next to the factorial just count down to 1, multiplying each number together. So if you see 5!, all this means is 5 x 4 x 3 x 2 x 1 = 120.

Factorials are sometimes seen explicitly (as in the problem below.) Oftentimes, you will need to use them when solving a difficult subset of math problems known as combination/permutations.

For now, try this problem:

Column AColumn B
7!6! + 6! + 6! + 6! + 6! + 6! + 6!

 

  1. The quantity in Column A is greater
  2. The quantity in Column B is greater
  3. The two quantities are equal
  4. The relationship cannot be determined from the information given

You can work this out the long way: 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1. Then you can do the same for column B, multiplying out and then adding the 6!s. Of course, if you catch yourself doing too much math always know there is a shorter way. In fact, quantitative comparison is testing your logical approach, so do as little math as possible.

Here, we can see that column B is made up seven 6!, or 7(6!), which equals 7 x 6 x 5 x 4 x 3 x 2 x 1 = 7!.  Therefore the two columns are equal.

Next time I touch on factorials will be in the context of permutation/combination problem, but as long as you understand the above you will be able to approach these more difficult problems.

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