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.
Is (4 ^x )^ (5−3x) =1 ?
(1) x is an integer.
(2) The product of x and positive integer y is not x.
If we modify the original condition and the question, we ultimately want to know whether 4^x(5-3x)=1=4^0, x(5-3x)=0, so whether x=0 or x=5/3.
There is only one variable, so we only need one equation, when 2 equations are given from the 2 conditions; there is high chance (D) will be our answer.
For condition 1, the answer becomes 'yes' for x=integer=0, but 'no' when x=1. This condition is insufficient.
For condition 2, on the other hand, we get xy=/=x, x(y-1)=/=0, so likewise, the answer to the question becomes 'yes' for x=5/3 and y=2, but 'no' for x=3 and y=2. This is, again, insufficient.
Combining the 2 conditions, the answer becomes 'no' for all x=1,2,3....... This is sufficient, so the answer becomes (C). This type of question is no longer asked in the test.
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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