Column Simplification and Algebraic Manipulation
Quantitative Comparison questions present two quantities (Column A and Column B) and ask whether A is greater, B is greater, they are equal, or the relationship cannot be determined. The advanced strategy is to simplify both columns toward a common form before comparing — this prevents the common mistake of computing both columns separately and then comparing, which wastes time and introduces arithmetic errors. The key manipulation rules: you can add the same value to both columns without changing the relationship; you can subtract the same value from both columns; you can multiply or divide both columns by the same positive value. Warning: multiplying or dividing by a negative value reverses the inequality, so this is only safe when the sign of the multiplier is known to be positive. Column simplification example: Column A = 3x + 12, Column B = 5x + 6, given x > 0. Subtract 3x from both: Column A becomes 12, Column B becomes 2x + 6. Subtract 6: Column A = 6, Column B = 2x. Divide both by 2: Column A = 3, Column B = x. Since x > 0 is given, we cannot determine whether x is greater than, equal to, or less than 3 — the answer is D. Without simplification, many students would attempt to compute specific values and miss this ambiguity. Algebraic simplification makes the relationship's dependency on variables explicit.