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.
Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?
(1) The median of the numbers in Set S is 0
(2) The sum of the numbers in set S is equal to the sum of the numbers in set T
When there are consecutive integers in an original condition, you only need to know the first number of variable. So, there is 1 variable in this case. That is, you need to know the first starting number of set S and set T, which is S={n-2,n-1,n,n+1,n+2}, T={m-3,m-2,m-1,m,m+1,m+2,m+3}. And there are 2 variables(n, m), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), it becomes S={-2,-1,0,1,2,3}, T={-3,-2,-1,0,1,2,3} -> yes. In S={n-2,n-1,n,n+1,n+2}, T={m-3,m-2,m-1,m,m+1,m+2,m+3}, 5n=7m. That is, n=7, m=5. So, S={5,6,7,8,9}, T={2,3,4,5,6,7,8} is no and not sufficient. Therefore, the answer is C.
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, there is 70% chance that C is the answer, while E has 25% 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 C 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, D or E.
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