In the expression \(a \$ b,\) the \(\$\) symbol represents one of the following arithmetic operations on \(a\) and \(b\)

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In the expression \(a \$ b,\) the \(\$\) symbol represents one of the following arithmetic operations on \(a\) and \(b\) (in the order the variables are shown): addition, subtraction, multiplication, and division. Given that it is not true that \(a \$ b = b \$ a\) for all possible values of \(a\) and \(b,\) a pair of nonzero, non-identical values for \(a\) and \(b\) is chosen such that \(a \$ b\) produces the same result, no matter which of the operations (under the given constraints) that \(\$\) represents. The nonzero value of \(b\) that cannot be chosen, no matter the value of \(a\), is

A. \(-2\)

B. \(-1\)

C. \(-\dfrac12\)

D. \(1\)

E. \(\dfrac12\)

Answer: D

Source: Manhattan GMAT