Smita04 wrote:
A quadrilateral is inscribed in a circle. If the circumference of the circle is 5(pi), what is the area of the quadrilateral?
(1) The length of one of the diagonals of the quadrilateral is 5.
(2) The length of two opposite sides are 3 and 4 respectively.
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.
A quadrilateral is inscribed in a circle. If the circumference of the circle is \(5\pi\), what is the area of the quadrilateral?
(1) The length of one of the diagonals of the quadrilateral is \(5\).
(2) The length of two opposite sides are \(3\) and \(4\) respectively.
In order to identify a quadrilateral on a specific circle, we need the lengths of 3 sides. It means we have 3 variables and 0 equation. However the first condition has 1 equation and the second condition has 2 equations. Thus when we consider both conditions together, they are sufficient.
Normally for cases where we need 2 more equations, such as original conditions with 2 variables, 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 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.
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