Problems based on Numbers Test 4

The 4 digit number 13b7 is divisible by 11.
Sum of odd numbers - Sum of even number = 0, or 11
$\left(1+\mathit{b}\right)-\left(3+7\right)=0$ or 11
$1+\mathit{b}-10=0$ or 11
b - 9 = 0 or b - 9 = 11
b = 9 or b = 20 rejected because b is a single digit number.
Now, 1,397 is 4 digit number.
The three digit number is 4a3 added to 984, obtaining 1,397.
Value of a = 1,397 - 984 = 4 a 3
9 - 8 = a
1 = a
Value of 3a + 4b = 3(1) + 4(9) = 3 + 36 = 39.