Let a # b = a²

Quantity A: x # 2
Quantity B: x # 3

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.


The correct answer is (C), the two quantities are equal. The defined function, the pattern defined in the problem introduction, simply says to take the first item a and square it. Note that b plays no active role in the defined function.

So x # 2 will equal x² and x # 3 will also equal x². Note that, just as b played no active role in the pattern provided, the numbers 2 and 3 following the # sign play no active role in determining x # 2 or x # 3. Therefore, the two expressions are identical and the answer is (C).
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It is stated:
a # b = a²
Then why a variable x is included in the comparison?

Quantity A: x # 2
Quantity B: x # 3

a # b = a² is the definition of the operation #, where instead of <i>a</i> and <i>b</i> we can plug numbers, values, expressions.

x # y = x²
18 # 4 = 18²
(x + 1) # 10 = (x + 1)²
10 # (x + 1) = 10²