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A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) =?

Correct Answer: 10

Explanation:

 4 a 3  |
 9 8 4  }  ==> a + 8 = b  ==>  b - a = 8  
13 b 7  |
Also, 13 b 7 is divisible by 11   ⟹   (7 + 3) - ( b + 1) = (9 - b )

⟹   (9 - b) = 0


⟹   b = 9


∴ (b = 9 and a = 1)    ⟹ (a + b) = 10.


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