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 = x
2+ 2xy + y
2
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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Video Lessons and 10 Fully Explained Grand Tests
Large number of solved practice MCQ with explanations. Video Lessons and 10 Fully explained Grand/Full Tests.