Question

Is xy \(<\) 15? 
Statement I - \(0.5 < x < 1\), and \(y^2\) = 144. 

Statement II - \(x < 3, y < 5\).

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both, statement I and statement II are needed to answer the question.
• D. If the question cannot be answered even with the help of both the statements.

Hint:

When faced with inequalities or equations, solve for the variables first and check if the result satisfies the given condition.

Answer 1

The Correct Option is A

From Statement I: \(0.5 < x < 1\), and \(y^2\) = 144.
Since \(y^2\) = 144, y = ±12.
So, we know that x is between 0.5 and 1, and y is either 12 or -12.
Therefore, xy is between 0.5 * 12 = 6 and 1 * 12 = 12, so xy is definitely less than 15.
Thus, Statement I alone is sufficient to answer the question.