for all integers W and F. What is 4 ψ 3?
Another type of GRE formula problem involves the use of strange symbols. In these problems, the GRE introduces an arbitrary symbol, which defines a certain procedure. These problems may look confusing because of the unfamiliar symbols. However, the symbol is irrelevant. All that is important is that you carefully follow each step in the procedure that the symbol indicates.
A technique that can be helpful is to break the operations down one-by-one and say them aloud (or in your head)—to “hear” them explicitly. Here are some examples:
| Formula Definition | Step-by-Step Breakdown |
| x ♥ y = x2 + y2 − xy | “The first number squared, plus the second number squared, minus the product of the two …” |
| s ○ t = (s − 2)(t + 2) | “Two less than the first number times two more than the second number …” |
| x is defined as the product of all integers smaller than x but greater than 0 … | “… x minus 1, times x minus 2, times x minus 3 … Aha! So this is (x − 1) factorial!” |
Notice that it can be helpful to refer to the variables as “the first number,” “the second number,” and so on. In this way, you use the physical position of the numbers to keep them straight in relation to the strange symbol.
Now that you have interpreted the formula step-by-step and can understand what it means, you can calculate a solution for the formula with actual numbers. Consider the following example:
The symbol
between two numbers indicates the following procedure: Take the square root of the first number and then raise that value to the power of the second number:
Watch for symbols that invert the order of an operation. It is easy to automatically translate the function in a “left to right” manner even when that is not what the function specifies:
for all integers W and F. What is 4 Φ 9?
It would be easy in this example to mistakenly calculate the formula in the same way as the first example. However, notice that the order of the operation is reversed—you need to take the square root of the second number, raised to the power of the first number:
More challenging strange-symbol problems require you to use the given procedure more than once. For example:
for all integers A and B. What is 2 Φ(3 Φ 16) ?
Always perform the procedure inside the parentheses FIRST:
Now you can rewrite the original formula as follows: 2 Φ (3 Φ 16) = 2 Φ 64.
Performing the procedure a second time yields the answer:
A Δ B = AB + B for all integers A and B. What is the value of −2Δ(3 Δ 1)?
for all integers s and t. What is the value of 2λ16?