20. a ≠ 0 Quantity A: x/a Quantity B: (a^-1)x
Answer: C
The two quantities are equal.
Both Quantity A and Quantity B simplify to the same expression, which is x/a. Therefore, they are equal to each other.
A) Quantity A is greater.
This option is incorrect because both quantities simplify to the same value, x/a. There is no basis to conclude that Quantity A is greater than Quantity B since they are equal.
B) Quantity B is greater.
This option is also incorrect. Similar to Quantity A, Quantity B simplifies to x/a. Therefore, it cannot be greater than Quantity A since they represent the same value.
C) The two quantities are equal.
This option is correct as both Quantity A (x/a) and Quantity B ((a^-1)x) represent the same mathematical expression. Since a^-1 is equivalent to 1/a, both quantities are indeed equal.
D) The relationship cannot be determined from the information given.
This option is incorrect because the simplification of both quantities allows us to determine their relationship definitively. Since they reduce to the same expression, we can clearly see that their relationship is one of equality.
Conclusion
The correct answer is that the two quantities are equal, as both simplify to x/a. All other options either assert an incorrect relationship or fail to recognize the equality established through simplification. Thus, the relationship is definitively determined.