Question

Is the polygon MNOPQRSTUVWXYZ regular?
Statement 1: MN + OP = QR + ST
Statement 2: MN + OP + WX ≠ QR + ST + YZ

• A. statement (1) alone is sufficient to answer the question
• B. statement (2) alone is sufficient to answer the question
• C. both the statements together are needed to answer the question
• D. statement (1) alone or statement (2) alone is sufficient to answer the question
• E. neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is B

To determine if the polygon MNOPQRSTUVWXYZ is regular, we need to analyze the provided statements. A regular polygon is one in which all sides are equal in length and all interior angles are equal.

Statement 1: MN + OP = QR + ST

This statement implies that the sum of certain pairs of sides is equal. However, it does not provide any information about whether all the sides of the polygon are equal. Therefore, this information is insufficient to conclude if the polygon is regular.

Statement 2: MN + OP + WX ≠ QR + ST + YZ

This statement indicates that the sum of some sides (MN, OP, WX) is not equal to the sum of other sides (QR, ST, YZ). This inequality suggests that the sides of the polygon are not all equal. Therefore, the polygon cannot be regular if the sides differ in length.

Conclusion

Statement 2 alone is sufficient to conclude that the polygon MNOPQRSTUVWXYZ is not regular, as it directly indicates the inequality of side lengths. Thus, the correct answer is: statement (2) alone is sufficient to answer the question.