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.
Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is 5 units. What is the area of the triangle?
1. The sides of triangle ABC are in the ratio 1 : 1 : root 2
2. The hypotenuse AC is 10 units
Transforming the original condition and the question, we have the below image.
In case of the triangle we have 3 variables and 2 equations (ang B=90 degree , BD=5) thus we need 1 more equation to match the number of variables and equations. Therefore there is high probability that D is the answer.
In case of 1), from 1:1:root2, we have root2*AC=5 and thus the length of AC. Then we have AB=BC=5root2, therefore the area is (1/2)(5root2)^2=25. The condition is sufficient.
In case of 2), we have AC=10 but no information regarding the length of AB,BC. Therefore the condition is not sufficient.
The answer is A.
Normally for cases where we need 1 more equation, such as original conditions with 1 variable, or 2 variables and 1 equation, or 3 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.
Attachments
GC DS soaringAlone Triangle ABC (20150913).jpg [ 11.92 KiB | Viewed 58407 times ]