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Re: Does x = 2? (1) x is a number such that x^2 3x + 2 = 0. (2) x is a
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07 Oct 2015, 23:11
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.
Does x = 2?
(1) x is a number such that x^2 – 3x + 2 = 0.
(2) x is a number such that x^2 – x – 2 = 0.
There is one variable (x) from the original condition, which means we need one equation in order to match the number of variables and that of the equations. The conditions gives us two equations in total, giving us high chance that (D) is going to be our answer.
Looking at condition 1, x^2-3x+2=0, (x-2)(x-1)=0, so x=1,2, but this condition alone is insufficient as it does not give a unique answer.
Looking at condition 2, x^2-x-2=0, (x-2)(x+1)=0, so x=-1,2. This condition is insufficient as well, as it does not give a unique value of x as well.
However, combining the 2 conditions, the answer becomes x=2. The 2 conditions are sufficient only when combined together, giving a unique answer. Therefore, the answer becomes (C).
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.