Given that,
Six Cars ( A, B, C, D, E, F) and Six Places (1, 2, 3, 4, 5, 6) and cars (A, B) are parked together.
To find: Is Car F at 1?
Statement 1: B and C both parked at even-numbered spaces.Even number spaces available: 2, 4, 6
Let (B, C) be at (2 & 4) in any order, then since (A, B) are together, the possible places for A can be at (1, 3, 5)
Let (B, C ) be at (4 & 6) in any order, then since (A, B) are together, the possible places for A can be (3,5)
Let (B, C) be at (2 & 6) in any order, then the possible places for A can be (1, 3, 5)
But in all the cases, we don't know anything about the positions of D, E & F.
Hence, this statement alone is
Insufficient.Statement 2: D and E both parked at odd-numbered spaces.Odd-number spaces available: 1,3,5
Let (D, E) be at (1, 3) or (1,5) in any order, then since place 1 is occupied by either D or E, hence car F can't be parked there anymore.
Let (D, E) be at (3,5) in any order, also (A, B) need to be parked together, hence the only possible options for A, B together are (1,2), thus in this case as well, F can't be parked at 1.
Thus, in all the cases F can't be parked at 1.
Hence this Statement alone is
Sufficient.Thus, the final answer is
B. Statement 2 alone is sufficient, but Statment 1 is not