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No question type divides students more than symbolism.  Some students have seen symbolism questions many times before and are quite comfortable with them.  These students may even think of symbolism questions as functions, which is correct, though unnecessary for purposes of the GMAT.

However, for students who have not come across symbolism questions before preparing for the GMAT, these problems can be among the most conceptually difficult on the exam.

All symbolism questions will invent some symbol.  The symbol will not apply to any math outside of the specific problem – the GMAT is testing your ability to take a novel rule and apply it.  Generally, the question stem will define the symbol as a specific operation and then expect the test taker to apply this definition to a specific instance.

For example @ is not a mathematical symbol of any sort, but a symbolism question could tell you that @x = x + 2.  This means that any time you see a number after the @ symbol you should add 2 to it.  The result will be equal to @(your number).  Let’s say the problem asks for the value of @5.  To solve, substitute 5 in for x.  Since @x = x + 2, @5 = 5 + 2 = 7.  Thus, you know that @5 = 7.

On the GMAT the operations will be a bit more complicated than the example listed above, however, the same principle applies.  Substitute out the variable given by the operation and substitute in the number given by the problem.  No matter how complex the operation appears, this strategy will always lead you to the right answer.

Keeping this in mind, try the data sufficiency problem below.

Problem:

For all non-zero integers n, . what is the value of x?

(1) x* = x

(2) x* = -2 – x

Answer:

Plugging x into the expression we have that .

The easiest way to solve this would to be to have a value for x .

Statement 1:

• If x * = x,  then .
• Multiplying both sides by x gives .
• Subtracting x + 2 from both sides leaves
• Using reverse FOIL gives you ( x -  2)( x + 1) = 0, That is, x = 2 or x = -1
• Since there are two possible answers, statement 1 is insufficient

Statement 2:

• If x * = -2 - x then
• Multiplying both sides by x gives
• Subtracting from both sides leaves
• Using reverse FOIL gives you ( x + 2)( x + 1) = 0. That is, x = – 2 or x = – 1.
• Once again, since there are two possible answers, statement 2 is insufficient

Combining Statements 1 & 2

• Statement 1 tells you x = 2 or -1
• Statement 2 tells you x = – 2 or – 1
• x = – 1 since it is the only common answer to both statements

The answer is C