Solution

25443

First name
Jamal David Wise
School
John Betts Primary School
Age
10

A3 is the only one that will work, because:
A0 has multiples of 2 with 1 added, and 1000-1 is 999, indivisible by 2.
A1 has multiples of 4 with 2 added, and 1000-2 is 998, indivisible by 4.
A2 has multiples of 8 with 4 added, and 1000-4 is 996, indivisible by 8.
A3, however, has multiples of 16 with 8 added, and 1000-8 is 992, a number which is divisible by 16.
A4 has multiples of 32 with 16 added, and 1000-16 is 984, indivisible by 32.
A5 has multiples of 64 with 32 added, and 1000-32 is 968, indivisible by 64.
A6 has multiples of 128 with 64 added, and 1000-64 is 936, indivisible by 128.
A7 has multiples of 256 with 128 added, and 1000-128 is 872, indivisible by 256.
None of the rest will work, because A8, for example, has multiples of 512 with 256, and 512*2 is 1024, already too big.