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.
What is the median of a set of 10 positive integers?
(1) The numbers are in an AP with the first term being 10
(2) The arithmetic mean of these 10 numbers is 45
In the original condition, there are 10 variables, which should match with the number of equations. So you need 10 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), L=80 is derived from (10+L)/2=45. Then, you can figure out the 10 variables, which is sufficient. C is the answer.
In fact, this is an integer question, which is one of the key questions and apply the mistake type 4. However, you can't apply the mistake type in this case.
Therefore, the answer is C.
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 (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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