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When x and y are integers, is x an even number? 1) 2x+y is

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by Max@Math Revolution » Thu Mar 17, 2016 5:24 pm
When x and y are integers, is x an even number?

1) 2x+y is an odd number.
2) 5x+3y is an odd number.


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Source: — Data Sufficiency |
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by Max@Math Revolution » Mon Mar 21, 2016 3:23 am
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.

When x and y are integers, is x an even number?

1) 2x+y is an odd number.
2) 5x+3y is an odd number.


In the original condition, there are 2 variables(x,y), 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), 2x becomes even and y=odd. If y=odd, 5x+3y=odd -> x=even, which is yes and sufficient.
Therefore, the answer is C.
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