Set A contains distinct integers: A = {2,4,6,-8,x,y}. When two numbers

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.

Set A contains distinct integers: A = {2, 4, 6, -8, x, y}. When two numbers from this set are picked and multiplied, what is the probability that the product is less than zero?

(1) x*y is not equal to zero.
(2) |x| = |y|


In the original condition, there are 2 variables(x,y), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), since x and y are distinct and one of them from x and y is negative, the number of positive numbers are determined by the total multiplication. It is unique and sufficient. However, this is an integer and probability question, which is one of the key questions. Apply the mistake type 4(A).
For 1), x>0, y>0 or x>0, y<0, which is not unique and not sufficient.
For 2), x=y or x=-y, which is distinct. So, only x=-y is possible and it determines the number of negative numbers, which is unique and sufficient.
Therefore, the answer is B not C.


 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.