Question

Is \( x = y \)?
A. \[ (x + y) \left( \frac{1}{x} + \frac{1}{y} \right) = 4 \] B. \[ (x - 50)^2 = (y - 50)^2 \]

• A. The question can be answered by one of the statements alone but not by the other.
• B. The question can be answered by using either statement alone.
• C. The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. The question cannot be answered even by using both statements together.

Hint:

Use algebraic identities to simplify equations and verify if the required conditions are met.

Answer 1

The Correct Option is B

In statement B, \( (x - 50)^2 = (y - 50)^2 \), which simplifies to \( x = y \) or \( x = 100 - y \). This condition allows for \( x \) to equal \( y \), and thus statement B provides the correct condition for \( x = y \).