Two different numerical choices lead to two different relationships between the quantities.ģ) On this one, picking numbers won’t get us very far. Now, try n = 4.įor this choice, they are equal. So, for this choice, quantity B is bigger. Best of luck! Practice problem explanationsġ) When both quantities are positive, as these are, we are allowed to square both quantities, because for positive numbers, squaring preserves the order of inequality.Ģ) This one is relatively straightforward and lends itself well to picking numbers. If the above paragraph gave you some flashes of insight, you may want to give the problems above another look before reading the solutions below. You will see some examples of this in the solutions below. If I suspect that, I have to use logic or mathematical reasoning to verify. If I pick 3, or 5, different values, and each one makes Quantity A bigger, that’s no guarantee: I can’t rely on picking numbers alone to verify, beyond doubt, that (A) or (B) or (C) is the answer. Remember, (D) is the answer about 25% of the time. As soon as two different choices lead to two different relationships of the quantities, then I know that (D) is the answer.
You see, suppose I plug in one value of x and find, say, that Quantity A is bigger, and then I pick another value, and find, say, that the two quantities are equal. If you are not running out of time, and have the ordinary time to devote to a QC question, then picking numbers, alone, will only be definitively helpful when the answer is (D).
That would allow you to performed leveraged guessing in a very short amount of time. I have effectively eliminated both (B) & (C) as answers. If you are running out of time, and need to guess, then picking numbers is very efficient: for example, if I pick one value for x, plug it in, and find, say, that Quantity A is bigger, then the answer has to be (A) or (D).
We cannot multiple or divide by a variable unless we are guaranteed that the variable is always positive.ģ) Picking numbers? This strategy is not nearly as helpful on algebraic QCs as it is on algebraic multiple choice. With multiplication and division, we have to be guaranteed that the number is positive: we can multiply or divide both sides by any positive number. We can always add the same number to both quantities, or subtract the same number from both quantities: we can add or subtract anything, no limits. In a QC, the relationship between the two quantities could be an inequality, so we must restrict ourselves to what we can do to both sides of an inequality. Inequalities have a few more restrictions. If you find yourself getting sucked into a tedious, time-consuming calculation, probably you are doing something the long hard way.Ģ) Matching operations: With equations, you can always do the same thing to both sides of an equation. The GRE is keenly interested in your ability to use logic and mathematical thinking to find shortcuts that radically simplify the comparisons in the QC. The GRE is not interested in your ability to perform detailed, time-consuming calculations. You don’t have to perform a detailed calculation. 1) Compare, don’t calculate: Your job is to figure out which quantity is bigger, or whether they are equal.
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