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.

23 students appeared for the Geography paper. What is the sum of marks obtained by them?

(1) The average mark obtained by the students equals the median mark obtained by the students

(2) The top 12 students have an average of 84 marks and the bottom 12 students have an average of 62 marks

There are 23 variables (23 students) and we require 23 equations in order to match the numbers, but only 2 equations are given; this makes (E) likely to be the answer.

If we look at the conditions together, the total average =(12*84+12*62)/(12+12)=73=median, so the total sum becomes 12*84+12*62-73=1679. The conditions provide a unique answer, therefore they are sufficient and the answer becomes (C)

For cases where we need 3 more equation, 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 (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

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