Hi @pizzanoodle !
Which area are you in? What are your target grammar schools?
Which types of entrance exam papers would your child face?
In answer to your questions, a lot depends on the nature and level of difficulty of the entrance exam papers and also the likely academic quality and volume of the competition.
For our child's school it was a case of a distinctive admission process for just one school. There were some 3,000 applicants for 100 places, with around 500 applicants of very high quality. There were four papers over two stages, with 300 out of the 3,000 qualifying for the two Stage 2 exam papers. The Stage 1 exam papers had brutal time pressure and some very difficult questions; one of the Stage 2 papers was essentially a GCSE style paper. The final scores were calculated to two decimal places as there was almost nothing to separate, say, Rank 60 from Rank 160.
So we used a Tutor and it worked very well.
Our top target school's prep was so hard and yet, once our daughter got used to that standard of working, the other schools' entrance exams proved straightforward. A new and different work ethic was established and she discovered what hard work could achieve - she could operate at a much higher level than any teacher at her primary school had ever let on! After that, the work at the grammar school itself held no fears and it all came naturally to her. She also learned eventually that every pupil starting at that school had been tutored and none found the school too tough.
For my two nephews - in a another part of the country - it was very different. The entrance exam prep was much easier but they still used a Tutor and both were successful. All their peers, too, had been tutored and none found that school too tough, either.