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If a square with 20 as one side’s length and decreases to

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by Max@Math Revolution » Mon Mar 21, 2016 5:30 pm
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If a square with 20 as one side's length and decreases to a and b shown as above figure, what is the area of the region shaded?

1) (a+b)^2=49
2) (a^2)+(b^2)=25


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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu Mar 24, 2016 3:55 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 a square with 20 as one side's length and decreases to a and b shown as above figure, what is the area of the region shaded?

1) (a+b)^2=49
2) (a^2)+(b^2)=25


When you modify the original condition and the question, 20^2-(a^2/2)-(b^2/2)=400-(a^2+b^2)/2 is derived, which makes 2) sufficient.
Thus, B is the answer.
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