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
How many positive factors does the positive integer x have?
(1) x is the product of 3 distinct prime numbers.
(2) x and 3^7 have the same number of positive factors.
There is 1 variable (x) in the original condition. In order to match the number of variables and the number of equations, we need 1 equation. Since the condition 1) and 2) each has 1 equation, there is high chance that D is the answer.
In case of the condition 1), we can get x=2*3*5. The number of distinct factors is (1+1)(1+1)(1+1)=8. The answer is unique and the condition is sufficient.
In case of the condition 2), if x and 3^7 have the same number of positive factors, then the number of distinct factors is (7+1)=8. The answer is unique and the condition is 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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