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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) = ?

10
11
12
15
Explanation:

4 a 3 |

9 8 4 } ==> a + 8 = b ==> b - a = 8

13 b 7 |

Also, 13b7 is divisible by 11   $\Rightarrow$   (7 + 3) - (b + 1) = (9 - b)

$\Rightarrow$   (9 - b) = 0

$\Rightarrow$   b = 9

$\therefore$ b= 9 and a= 1    $\Rightarrow$ (a + b) = 10.

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