Question 19

The two quantities are equal.

The equation 1/x - 1/y = 1/(xy) implies a relationship between x and y that leads to the conclusion that both quantities are equal under the condition that xy is not zero. This can be rearranged and solved to show that x and y must be equal for the equation to hold true.

A) Quantity A is greater.

This option is incorrect because the equation derived from the initial expression indicates that the values of x and y must be equal to satisfy the equality. If Quantity A were greater, the equation would not hold.

B) Quantity B is greater.

This option is also incorrect for the same reason as option A. If Quantity B were greater than Quantity A, then the equation would not satisfy the condition of equality, contradicting the relationship established by the equation.

C) The two quantities are equal.

This option is correct because the manipulations of the initial equation show that x and y must be equal for the equation 1/x - 1/y = 1/(xy) to hold true. Thus, both quantities represent the same value.

D) The relationship cannot be determined from the information given.

This option is incorrect because the information provided in the equation allows for a definitive conclusion about the relationship between x and y. The equation clearly indicates that x and y must be equal, eliminating any ambiguity.

Conclusion

The correct answer is that the two quantities are equal because the equation directly implies this relationship. All other options fail as they suggest inequalities or indeterminacy, which contradicts the derivation from the initial equation. Hence, the only logical conclusion is that Quantity A and Quantity B are equal.