The number 2A5A0A2 is divisible by 99. What is the digit A

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

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step-by-step explanation:

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