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If r and s are positive integers, when r+s is divided by 3,

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by Max@Math Revolution » Tue Feb 16, 2016 12:58 am
If r and s are positive integers, when r+s is divided by 3, what is the remainder?

1) rs is divisible by 9
2) s is divisible by 3


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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu Feb 18, 2016 5:53 pm
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If r and s are positive integers, when r+s is divided by 3, what is the remainder?

1) rs is divisible by 9
2) s is divisible by 3


In the original condition, there are 2 variables(r,s), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), r=s=3 -> yes, r=1, s=9 -> no, which is not sufficient.
Therefore, the answer is E.
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