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 equations ensures a solution.
If ax^2 + bx^3 = 5, where a and b are non-zero numbers, what is the value of a + b?
(1) ax^2 = a
(2) bx^3 = b
Transforming the original condition and the question we have 3 variables (a,b,x) and 1 equation (ax^2 + bx^3 = 5). Since we need to match the number of variables and equations,we need 2 more, therefore C is likely the answer. Using both 1) & 2) together, ax^2 + bx^3 = 5--> a+b=5 thus the answer is C. However, this is a 'trivial' case and thus is not our answer. Therefore using common mistake type 4(A),
1) ax^2=a--> x=-1,1. Substituting x=-1 to ax^2+bx^3=5 we have a-b=5 thus a=6, b=1 or a=7, b=2. Our answer is a+b=7,9..etc which is not unique and therefore not sufficient.
2) bx^3=b --> b=1, thus substituting it inside ax^2 + bx^3 = 5 gives us a+b=5. the answer is unique, therefore the answer is B.
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