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

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Source: — Data Sufficiency |

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by ceilidh.erickson » Wed Nov 22, 2017 12:17 pm
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.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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