Which indirect sentence is correct?

Question

"You had better sell the house," Tom said
Tom suggested that I sold / should sell the house (this is the answer of A Practical English Grammar written by A.J. Thomson and A.V. Martinet)
Tom suggested that I sell / should sell the house (This is the answer of FCE use Of English written by Virginia Evans)

As you see, we have two different ansers here. A Practical English Grammar says we have to use " suggested that + subject + past tense or should" while the other grammar book FCE says we can use "suggested that + present tense or should ". Both of the books say we can use should + infinitive after "suggested that". This is okey, no problem here but one of them says we have to use presnt tense (sell) while the other says we have to use past tense (sold). Which of them is correct?...Thanks for your answers...

Answer 1

This one is OK

..... Tom suggested that I should sell the house

This one is not correct

..... Tom suggested that I sold the house

This one is OK

..... Tom suggested that I sell the house

Answer 2

i'm specific that the present stressful could want for use for this reason. the only time the previous stressful could be used is that if Tom have been attempting to describe, with out data, why the homestead's deed replace into now no longer on your call; i.e. "whilst asked why my family homestead replace into occupied via a prolonged family of Norwegian elk herders, Tom suggested that I possibly bought the homestead." i haven't heard, in British or American English, a single occasion of the previous stressful getting used as a advice in the type you describe.