A four digit number is AB40 is divisible by 9 where A and B satisfying

1.	A four digit number is AB40 is divisible by 9 where A and B satisfying A + B < 19, then find the possible number of pairs of (A, B).1. 102. 83. 114. 9
Answer» Correct Answer - Option 1 : 10 Concept Given number is divisible by 9, if the sum of the digits of the number is divisible by 9 Explanation Sum of the digits (A + B + 4 + 0) should be divisible by 9. For A + B + 4 = 9 The value of A + B = 9 - 4 = 5 A and B could be (5, 0), (2, 3), (3, 2), (1, 4), (4, 1) Note:- We cannot take A as 0, because at A = 0, the number is not a 4 digit number. For A + B + 4 = 18 The value of A + B = 18 - 4 = 14 So, value of A and B could be (7, 7); (6, 8); (8, 6); (9, 5)and (5, 9) This number could be 5040; 2340; 3240; 1440; 4140; 7740; 6840; 5940; 8640 and 9540 ∴ 10 pairs are possible. Note: Pair (0,5) is not considered, because if we 0 used as the first position Then we get 0540, 0540 is not the 4 digit value, it's a three-digit value. That's why we have not considered this pair.

A four digit number is AB40 is divisible by 9 where A and B satisfying A + B < 19, then find the possible number of pairs of (A, B).1. 102. 83. 114. 9

Answer» Correct Answer - Option 1 : 10

Concept

Given number is divisible by 9, if the sum of the digits of the number is divisible by 9

Explanation

Sum of the digits (A + B + 4 + 0) should be divisible by 9.

For A + B + 4 = 9

The value of A + B = 9 - 4 = 5

A and B could be (5, 0), (2, 3), (3, 2), (1, 4), (4, 1)

Note:- We cannot take A as 0, because at A = 0, the number is not a 4 digit number.

For A + B + 4 = 18

The value of A + B = 18 - 4 = 14

So, value of A and B could be (7, 7); (6, 8); (8, 6); (9, 5)and (5, 9)

This number could be 5040; 2340; 3240; 1440; 4140; 7740; 6840; 5940; 8640 and 9540

∴ 10 pairs are possible.

Note:

Pair (0,5) is not considered, because if we 0 used as the first position

Then we get 0540, 0540 is not the 4 digit value, it's a three-digit value.

That's why we have not considered this pair.