GMAT important Verified Instructor Notes for Exam Preparation

2 Linear Equations, 2 Variables, 1 Solution We learned back in 9th Grade that if you have 2 linear equations with 2 variables, there will always be one unique solution. For Data Sufficiency questions, we can seek out these equations in the stimulus and statements and (without calculating) know if we have enough information. For example, If the mileage on car X is currently exactly 3 times the mileage on car Y, what is the mileage on car X? (1) When each car had 6,000 miles less than they have now, car X had 4.5 times the mileage that car Y had. (2) When each car has 2,000 miles more than they have now, car X will have 2.75 times the mileage that car Y will have. Stimulus: x = 3y Statement 1: (x - 6000) = 4.5(y - 6000) Statement 2: (x + 2000) = 2.75(y + 2000) Visually, this is a lot easier than dealing with cars and mileage. Again, we do not need to calculate. Since an equation is GIVEN in the stimulus, we just need one more to find the unique solution for x. Each statement is sufficient. Choice (D). Caveat #2: Non-Linear Equations What is the value of x?