A nearby high-power HF broadcast station in the 31-metre band is interfering with your reception on the 40-metre and 30-metre bands. What type of filter is needed on the receiver to minimize interference?

The interfering broadcast station is in the 31-metre band (around 9.4 to 9.9 MHz). You want to operate on the 40-metre band (7 MHz) and the 30-metre band (10.1 MHz). Because the interference is geographically situated right between the two bands you want to use, you need a filter that removes only that middle chunk of spectrum. A band-reject filter is designed to block a specific, defined range of frequencies while allowing signals both below and above that range to pass through unimpeded. This perfectly fits the scenario of blocking 31 metres while passing 40 metres (below) and 30 metres (above). A low-pass filter would block the 30-metre band, and a high-pass filter would block the 40-metre band. A band-pass filter would only let one of your desired bands through while blocking the other.