Data Sufficiency

When k, l, and m are different positive integers greater than 1, k+l+m=?

1) km=15
2) kml=30


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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.

When k, l, and m are different positive integers greater than 1, k+l+m=?
1) km=15
2) kml=30


In the original condition, there are 3 variables, which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2), k+l+m=10 si derived from (k,l,m)=(3,2,5),(5,2,3), which is unique and sufficient. Then the answer is C. Since this is an integer question which is one of the key questions, apply the mistake type 4(A).
In case of 1), you don't know l, which is not unique and not sufficient.
In case of 2), in (k,l,m)=(2,3,5),(2,5,3),(3,2,5),(3,5,2),(5,2,3),(5,3,2), k+l+m=10 is derived, which is unique and sufficient. Therefore, the answer is B.


� 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.