Call 911: Some Digits are Missing

[dtweah]

Given that 29a031 × 342 = 100900b02 where a and b denote two missing
digits, what is the value of a + b ?
(a) 7
(b) 8
(c) 9
(d) 10
(e) 11

[dumb.doofus]

I just used basic multiplication to deduce a = 5 and b = 6

so a + b = 11

any other methods??

[dtweah]

I just used basic multiplication to deduce a = 5 and b = 6

so a + b = 11

any other methods??

I did the same but here is what they say in the OA

Recall the tests for divisibility by 9 and by 11. Since 342 is divisible by 9, the number 100900b02 is as well. So b has to be 6. But then 100900b02 is divisible by 11. Since 342 is not divisible by 11, we deduce 29a031 must be divisible by 11. So a has to be 5, and a + b = 11.