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.
In quadrilateral ABCD, sides AB and BC each have length √2, while side CD has length 2. What is the area of quadrilateral ABCD?
(1) The length of side AD is 2.
(2) The angle between side AB and side BC is 90°.
In the original condition,
there are 5 variables (4 sides and 1 diagonal line) and 3 equations(sides AB and BC each have length √2, while side CD has length 2) and thus we need 2 more equations to match the number of variables and equations. Since there is 1 equation each in 1) and 2), the best answer is C by our DS definition. However, this type of question always shows the diagram in actual exam. If diagram is not shown, E is the answer because we don't know the alphabetical orders of vertices (ABCD? ACBD? BDAC?)
Normally for cases where we need 2 more equations, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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