Hello Jane, The second part is definitely 'sing' because can (can not) is a modal verb and it must be followed by an infinitive. In the first part it is assumed that the people are still alive so this is actions in unfinished time so your answer is correct (have listened). We can't use the past simple 'listened' unless a time is specified - They listened to many Beatles song last year ..... Hope this helps

Unlike others, while I agree that the present perfect is the preferred choice here, I cannot agree that the simple present is either grammatically wrong without a specified time period or wrong here. Often, test questions require a "more or most likely" choice, and not an "only choice" response. Consider another setting: "They had an utter ball. They danced. They drank. They listened to shedloads of Beatles songs. But now it's come to karaoke time, and it turns out that they can't sing any of them."

You can use either listen (present tense) or listened (past tense). The option you choose will depend on WHEN "they" are doing the listening. If "they" are CURRENTLY listening to many songs but cannot sing any of them then you would say (listen). You would say (listened) if "they" PREVIOUSLY heard or listened to many songs. You do not say "have listened" because by using the past tense (listened) it is assumed the action happened in the past, thus removing the need for "have" which also denotes the past. Google "double negative example" so you can read the grammatical rule on this. I hope that made sense.