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 remainder when integer k is divided by integer j?
(1) j and k each have the same number of unique factors.
(2) 1 < j < k < 10
There are 2 variables (j,k) in the original condition, and we need 2 equations in order to match the number of variables. As 2 equations are provided from the 2 conditions, there is high chance that (C) is going to be the answer.
However, when looking at the conditions together,
The remainder becomes 1 when j=2, k=3, and
the remainder becomes 2 when j=3 and k=5. Hence, the conditions are insufficient giving no unique answer, and the answer becomes (E).
For cases where we need 2 more equation, 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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