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Lesson: qc03

Quantitative Comparisons Application of 6 Step Paln on Example

Column A
Column B

xy ? 0
x2+y2
(x+y)2

Explaination

This is a relatively difficult question. Approximately 40 percent of test-takers respond correctly to questions like this one. Here’s how to compare the two quantities, using the 6-step approach:
Step 1: This question involves quadratic expressions and squaring a binomial. Since there are two variables here (x and y) but no equations, you won’t be calculating precise numerical values for either variable. Take notice of the centered information, which establishes that neither x nor y can be zero (0).
Step 2: On their faces, the two quantities don’t appear to share common terms that you can simply cancel across quantities. But they’re similar enough that you can bet on revealing the comparison by manipulating one or both expressions.
Step 3: Quantity A is simplified, so leave it as is—at least for now. Square Quantity B:
(x+y)2 = x2+ 2xy + y2
Notice that the result is the same expression as the one in Column A, with the addition of the middle term 2xy. Now you can cancel common terms across columns, so you’re left to compare zero (0) in Column A with 2xy in Column B.
Step 4: The variables x and y can each be either positive or negative. Be sure to account for different possibilities. For example, if x and y are both positive or both negative, then Quantity B is greater than zero (0), and thus greater than Quantity A. However, if one variable is negative and the other is positive, then Quantity B is less than zero (0), and thus less than Quantity A.
Step 5: You’ve done enough work already to determine that the correct answer must be choice (D). You’ve proven that which quantity is greater depends on the value of at least one variable. There’s no need to try plugging in different numbers. The relationship cannot be determined from the information given.
Step 6: Check your squaring in step 3, and make sure your signs (plus and minus) are correct. If you’re satisfied that your analysis is correct, confirm your response and move on. The correct answer is (D).
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