Question: Is xy positive?<br>Statement-I: x=\sqrt{-0.19683}<br>Statement-II: y=\sqrt{x}

Consider the following for the next ten (10) items that follow : Each item contains a Question followed by two Statements. Answer each item using the following instructions : Choose option (a) If the Question can be answered by one of the Statements alone, but not by the other. (b) If the Question can be answered by either Statement alone. (c) If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone. (d) If the Question cannot be answered even by using both Statements together.

  1. A. If the Question can be answered by one of the Statements alone, but not by the other.
  2. B. If the Question can be answered by either Statement alone.
  3. C. If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone. ✓
  4. D. If the Question cannot be answered even by using both Statements together.

Correct Answer: C. If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

Explanation

Statement-I strictly defines x as the cube root of -0.19683. Since the cube root of any negative number is always negative, we conclude that x \lt 0. Statement-II establishes the relationship y = \sqrt{x}. Since x is negative, its cube root y must naturally also be negative, meaning y \lt 0. The multiplication of two negative numbers is always positive. To confidently determine that the sign of xy is positive, we need the sequential information from both statements combined.

Related questions on Algebra

Practice more CDS Elementary Mathematics questions