Maybe I'm reading the original question wrong,
You are missing the essential point of the question which stated:
An aeroplane maintains straight and level flight while the IAS is doubled.
The key parts are that level flight is maintained when IAS is doubled.
Doubling IAS without changing CL will produce 4 times as much lift. This will make the aircraft climb. So to maintain the left flight condition of the question the pilot must reduce angle of attack in order to reduce CL to 1/4 of its initial value.