What is the remainder when 5-digit positive integer...

[swerve]

What is the remainder when 5-digit positive integer pqpqp is divided by 3?

1) p=2
2) q=3

The OA is B.

Please, can any expert explain this DS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

[ceilidh.erickson]

There is a rule that says that any positive integer will be divisible by 3 if its digits add up to a multiple of 3. E.g. is 567 a multiple of 3? 5 + 6 + 7 = 18, so yes.

What is the remainder when 5-digit positive integer pqpqp is divided by 3?

1) p=2
Here, we can test numbers:
21212 divided by 3... (I picked this because 21 is divisible by 3, so it makes long division quicker): 7070 remainder 2

22222 divided by 3... 7407, remainder 1.

2 different remainders in 2 different scenarios --> insufficient.

2) q=3

If q =3, then pqpqp must be a multiple of 3. When we add up the digits, we'd get 3p + 6. That will be a multiple of 3 regardless of what p is. Therefore, the remainder will always be 0.

The answer is B.

Please also post the SOURCE of your question.