Statement : $W \le X, X \ge Y, Y < Z$
Conclusions: (I) $Z > X$
(II) $W > Y$
(III) $Y > W$
None of the conclusions (I), (II) and (III) are true.
To evaluate the truth of the given conclusions based on the statement, let's analyze each part:
Statement: W \le X, X \ge Y, Y < Z
Analysis:
- The first part of the statement W \le X implies that W is either less than or equal to X.
- The second part X \ge Y means X is greater than or equal to Y.
- The last part Y < Z indicates that Y is less than Z.
Conclusions:
- Z > X: The statement provides no direct comparison between Z and X. Y \lt Z and X \ge Y do not infer Z \gt X, as Z can be greater than or less than X. Therefore, Conclusion I is not definitely true.
- W > Y: From the statement, we have W \le X and X \ge Y, so W can indeed be lesser, equal, or greater than Y, but it is not definitively greater. Conclusion II is not definitely true.
- Y > W: According to the given statement, X \ge Y and W \le X; there is no definitive indication that Y is greater than W. So, Conclusion III is not definitely true.
Conclusion: None of the conclusions (I), (II), and (III) are definitely true.
Important Questions from Mathematical Inequalities
Which figure should replace the question mark (?) in the following series to continue the pattern?
Select the option that is related to the third term in the same way as the second term is related to the first term and the sixth term is related to the fifth term.
400 : 200 :: 248 : ? :: 256 : 128
Which of the following option figures will complete the pattern in the figure given below?
A square sheet of paper is folded along the dotted line successively along the directions shown and is then punched in the last. How would the paper look when unfolded?
Select the correct combination of mathematical signs that can sequentially replace the * signs and balance the given expression.
23 * 9 * 13 * 96 * 2 * 92
