Question 4: With a, b being natural numbers, if 10a + b is divisible by 13, then a + 4b is divisible by which of the following?

Consider 10.(a + 4.b) = 10.a+40.b = (10.a + b) + 39.b

Since (10.a + b) ⋮ 13 and 39b ⋮ 13, 10.(a + 4.b) ⋮ 13

Since 10 is not divisible by 13, it follows that (a + 4.b) 13

So if 10a + b is divisible by 13 then a + 4b is divisible by 13.