Question

Suppose A and B are digits such that the 4-digit number A37B is divisible by 36. What is
A + B?

Answer 1

Answer:

The answer is 10............

Answer 2

Answer: 8

Step-by-step explanation:

IF ‘a and b are digits’ then a and b could be 0, 1, 2, 3, 4, 5, 6,7, 8, or 9.

IF ‘a37b is a 4-digit number’ we conclude that a is not zero.

IF ‘a37b is divisible by 36’ then it is divisible by 2 and 3, moreover 4 and 9.

Divisibility rule by 4 states the the last 2 digits of the number must be divisible by 4 which means 7b could be 72 or 76.

Divisibility rule by 9 states that the sum of the digits must be a number divisible by 9; hence, a + b + 10 = M9 (M9 means multiple of 9) Subtracting 10 on both sides we get a + b = M9 - (9+1) = M9 - 1 (because a multiple of 9 minus a multiple of 9 = a multiple of 9). Therefore, a + b = 9 - 1 = 8

One step further, the number is 6372 (for a = 6 and b = 2) or 2376 (for a = 2 and b = 6),

Hence, the answers is 8