Explanation:

- Offhand typically means done or said without preparation or forethought. It suggests a casual or spontaneous approach.

- Option 1: Dazzling - This word means something that is extremely bright or impressive. It’s unrelated to the concept of preparation or spontaneity.

- Option 2: Lavish - Lavish means rich, elaborate, or luxurious. It doesn’t directly oppose offhand, which doesn’t inherently relate to extravagance.

- Option 3: Considered - Considered means carefully thought out or planned. This is the opposite of doing something offhand, which implies a lack of planning.

- Option 4: Brusquely - Brusquely means behaving in a blunt or direct manner and is more about the style of interaction rather than preparation.

The correct answer is:

- Option 3: Considered