Quite possibly the most intimidating problem on the GRE contains strange symbols: @, #, *, or a black circle often accompany these problems. Many recoil in horror thinking – I’ve never learned that before! (Or perhaps more aptly, what the @#?!)

But don’t despair – the symbols are completely arbitrary and are defined on the spot by the GRE. Here is an example:

#x# = . What is the value of #3# – #2#?

Again, the pound sign surrounding the number has no mathematical meaning outside the problem. For the question, you simply want to follow the rules. Here, wherever we see a number between the pound sign, such as #3#, we want to refer back to #x# = . The 3 essentially is taking the place of the x. So if #x# = , then #3# = .

Now do the same for #2#: .

So #3# – #2# =

Now let’s try another one. This time, though, I am going to put a little spin on it.

n^^ = , where n is a positive integer. For how many values of n is n^^ less than zero?

- 1^^
- 1^^ – 2^^
- 3^^
- 3^^ + 4^^
- 5^^ – 2^^

First off, note that ! is the factorial sign. It is not a strange symbol, but standard mathematical notation.You should quickly see that after n = 3, n^^ is going to yield a positive result. For example, , so 4^^ . So when n is greater than or equal to 4, n^^ is greater than zero.

Be careful: 1^^ = 0, so it is not less than zero. Therefore, there are two values (2, 3) for which n^^ is less than zero.

When we look at the answers, 2 is not among them. Instead, the strange symbol ^^ has been reintroduced. Therefore you have to figure out which answer choice equals 2, the number of values of n that are less than zero.

The answer is (B), which gives us 1^^ = 0 minus 2^^ = -2, so

Okay, that was a tough one. Let’s make the problem easier, while adding a layer of complexity – the embedded strange symbol.

If x is even, @x = ; if x is odd, @x = . What is the value of @(@(@5)?

- 21
- 40
- 63
- 117
- 140

Notice I’ve used the strange symbol three times. Don’t worry – just follow the operation (the technical name of this process). Taking the problem apart one step at a time, we get @5 = 8. @8 = 21, and @21 = 40. Just like that, B.

## Takeaway

Don’t be freaked out by strange symbols on the GRE. The question will always clearly define the symbol for you. Carefully follow the steps to the correct answer.

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