Happy Dads the issue is whether the child who got the scholarship got it because they were heavily tutored, or would have got it anyway? The indies are interested in ability and potential not cramming and go out of their way to devise exams that test the former not the latter.
In the case of LEH they ask on the application form if candidates have been tutored so that they can take it into account, and say that they can spot the telltale signs, so not being truthful is not a sensible way to go. They have a basic level of attainment in English and Maths below which they consider a pupil will not be able to comfortably cope with Year 7. If you are in a state school you may not have covered the entire curriculum so it makes sense to have covered that, and to have some help with working in timed conditions with a tutor or parent to be able to achieve that level of attainment, but it doesn't take heavy tutoring, or tutoring from Year 4. My own DD got a place with one terms tutoring.
However that is quite deliberately a fairly basic level, they consolidate in Year 7 to ensure the playing field is level for state and private school pupils. Then they interview all candidates who have that level of attainment and the interview, along with reasoning scores, general knowledge and the way that they have tackled the entrance exam are used to assess the pupil as a whole, their potential, creativity, personality, rather than just looking at attainment. None of that can be tutored for. It is why many of the Maths questions set are more tests of reasoning than attainment. To my knowledge only SPGS set the bar high in terms of attainment, and they set the bar high on everything else as well.
The old Head at Surbiton told a story of her exasperation that one year she had a whole bunch of candidates who when asked if they had any questions in the interview (expecting that an 11 year old might ask about trips or lunches or whatever) replied "if you could change one thing about your school what would it be" they immediately were put into the tutored pile.
Sorry OP to have gone off thread. I hope your DC is very happy at Christ's.