Answer:
A = 3
2A5A0A2 = 2353032
Step-by-step explanation:
Given:
2A5A0A2 is divisible by 9
2A5A0A2 can be divisible by 99 if the sum of the digits can be divided by 9
Digits A is between 0 to 9
2 + A + 5 + A + 0 + A + 2 = 9x
Where,
x = multiples of 9
9 + 3A = 9x
Make A the subject
A = (9x - 9) / 3
When x = 0
A = {9(0) - 9} / 3
= (0 - 9) /3
= -9/3
= -3
When x = 1
A = (9x - 9) / 3
= 9(1) - 9 /3
= 9-9/3
=0/3
A = 0
When x = 2
A = (9x - 9) / 3
= 9(2) -9 / 3
= 18-9/3
= 9/3
A = 3
When x = 3
A = (9x - 9) / 3
= 9(3) - 9 / 3
=27 - 9 /3
= 18/3
A = 6
When x = 4
A = (9x - 9) / 3
= 9(4) -9 /3
= 36-9/3
= 27/3
= 9
Recall, Digits A is between 0 to 9
Substituting A = 0
2050002 ÷ 99
= 20707.09
Substituting A = 3
2A5A0A2
2353032 ÷ 99
= 23,768
Substituting A = 6
2A5A0A2
2656062 ÷ 99
= 26,838.91
Substituting A = 9
2A5A0A2
2959092 ÷ 99
= 29,889.82
Therefore, the only A digit that will not give a decimal number when divided by 9 is 3
A = 3
