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.
If x and y are prime numbers, and n is a positive integer, what is the factors' number of xy^n?
1) xy=21
2) n=2
-> In the original condition, there are 3 variables(x,y,n), 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), 3(7^2) or 7(3^2) is derived. Then, the number of factors is (1+1)(2+1)=6, which is sufficient. Thus, C is the answer.
Note: when different prime numbers are given, the answer is most likely to be B.
-> When a word "different" is given, in 2) n=2, the number of factors is (1+1)(2+1)=6 from x(y^2), which is sufficient.
Therefore, the answer is B.
If x and y are prime numbers, and n is a positive integer, what is the factors' number of xy^n?
1) xy=21
2) n=2
-> In the original condition, there are 3 variables(x,y,n), 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), 3(7^2) or 7(3^2) is derived. Then, the number of factors is (1+1)(2+1)=6, which is sufficient. Thus, C is the answer.
Note: when different prime numbers are given, the answer is most likely to be B.
-> When a word "different" is given, in 2) n=2, the number of factors is (1+1)(2+1)=6 from x(y^2), which is sufficient.
Therefore, the answer is B.
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