2016 · Q58
Suppose R is the region bounded by the two curves Y = x^2 and Y = 2x^2 - 1 as shown in the following diagram (a lens-shaped region R between the two parabolas). Two distinct lines are drawn such that each of these lines partitions the regions into at least two parts. If 'n' is the total number of regions generated by these lines, then:
general-mental-abilityquantitative-aptitude
- A'n' can be 4 but not 3
- B'n' can be 4 but not 5
- C'n' can be 5 but not 6
- D'n' can be 6
Explanation
The region R between y = x^2 and y = 2x^2 - 1 is a curved, non-convex crescent (the parabolas meet at (+-1, 1) and the region bulges downward). Because of this curvature, a straight line can meet R in two disjoint segments, so two suitably placed lines can cut the crescent into 5 regions. However, no arrangement of two lines can produce 6 regions of this lens. Hence n can be 5 but not 6.