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.
n is the product of least and greatest 6 consecutive integers. What is n?
(1) The greatest integer is 20
(2) The average arithmetic mean of 6 consecutive integers is 17.5
In the original condition, you need to figure out the number of consecutive integers and the first integer. So, there are 2 variables. In this question, it’s given that there are 6 consecutive integers and you only need to figure out the first integer. Thus, there is 1 variable, which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), 15,16,17,18,19,20, which is unique and sufficient.
For 2), also 15,16,17,18,19,20, which is unique and sufficient.
Therefore, the answer is D.
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, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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