CAT 2003 Slot 1 — QA Question 33
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
In the figure below, ABCDEF is a regular hexagon and ∠AOF = 90°. FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF?
Answer & solution
- B
- C
- D
We can see that triangles AMF, AMB, BMC, CMD, DME and EMF are all equilateral triangles. Also, AE, XY and BD bisect MF, AB, ED and CM.
∴ All the small right triangles in the figure are congruent.
∴ A(âAOF) = × the area of the hexagon ABCDEF
Hence, option (a).