Discussion
The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order.
Consider the following statements:
- The line segment joining R and S is longer than the line segment joining P and Q.
- The line segment joining R and S is perpendicular to the line segment joining P and Q.
- The line segment joining R and U is parallel to the line segment joining T and Q.
Based on the above statements, which one of the following options is CORRECT?
Answer: A
The correct statement is The line segment joining R and T is parallel to the line segment joining Q and S.
In a regular hexagon there are three lengths: side, short diagonal and long diagonal. A long diagonal is perpendicular only to short diagonals, and a short diagonal is perpendicular to sides and long diagonals. Trying the possibilities, RS longer than and perpendicular to PQ, together with RU parallel to TQ, can only be met with RS a long diagonal and PQ a short diagonal.
Up to rotation and reflection the order round the hexagon is then forced: P, S, Q, U, R, T. Check: R and S are opposite; P and Q sit either side of S, so PQ is a short diagonal perpendicular to RS; RU is a side and TQ is the long diagonal parallel to it.
In this order RT and QS are opposite sides, so they are parallel. TQ and PU are two different long diagonals, so they meet at the centre and are not parallel. RP is a short diagonal, and UQ and QS are sides that each meet its direction at 30 degrees, not 90, so the two perpendicularity claims fail.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development