Question

What is the distance x between two cities A & B in integral number of kms?
Statement A
A. x satisfies the equation \( \log_2 x = \sqrt{x} \).
Statement B
B. \( x \leq 10 \) kms.

• 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:

When solving logarithmic and square root equations, use given constraints to find integer solutions.

Answer 1

The Correct Option is C

From Statement A: The equation \( \log_2 x = \sqrt{x} \) can be solved to find a possible value for \( x \), but we need further constraints to determine its integer value.
From Statement B: Knowing \( x \leq 10 \) helps us narrow down the possible solutions to integral values of \( x \). Combining both statements, we can solve for \( x \). Therefore, the Correct Answer is (3).