emmak wrote:
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. -1/2
D. 1
E. 1/2
I would like to have some discussion before posting the correct answer
Since it's NOT true that
a$b=b$a for all possible values of
a and
b, then $ is neither addition not multiplication (because \(a+b=b+a\) and \(ab=ba\) for all possible values of
a and
b).
So, we have that $ is either subtraction or division.
Next, we are told that
a$b produces the same result, no matter which of the operations (under the given constraints) that $ represents so no matter whether $ is subtraction or division
a$b will produce the same result, so \(a-b=\frac{a}{b}\) --> \(ab-b^2=a\) --> \(a=\frac{b^2}{b-1}\) -->
b cannot be 1, because in this case \(b-1=0\) and we cannot divide by zero.
Answer: D.
Hope it's clear.
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