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GRE Matching Operations A powerful QCQ strategy
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21 Jan 2022, 10:45
21 Jan 2022, 10:45
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Expert Reply
GRE Matching Operations – A powerful QCQ strategy
In GRE - Is testing values an overrated strategy to solve QCQ questions?, I explained the limitations of the QC strategy of testing values. In this article, we’ll examine an underrated strategy that just may become your favorite go-to approach when solving QC questions.
To set the stage, try answering this question:
Quote:
\(x > 2\)
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
\(\frac{(x^3 – x^2 + x - 6)}{(x^2 – 4)}\) |
\(x-1\) |
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
We’ll solve this question using Matching Operations. That is, what we do one quantity, we do to the other quantity.
Since \(x > 2\), we know that \(x^2 > 4\), which means \(x^2 – 4\) must be positive. So, we can safely multiply both quantities by \((x^2 – 4)\) to get:
Quote:
Quantity A |
Quantity B |
\(x^3 – x^2 + x - 6\) |
\((x^2 – 4)(x – 1)\) |
Expand Quantity B to get:
Quote:
Quantity A |
Quantity B |
\(x^3 – x^2 + x - 6\) |
\(x^3 – x^2 - 4x + 4\) |
Subtract \(x^3\) from both quantities to get:
Quote:
Quantity A |
Quantity B |
\(-x^2 + x - 6\) |
\(-x^2 - 4x + 4\) |
Add \(x^2\) to both quantities to get:
Quote:
Quantity A |
Quantity B |
\(x - 6\) |
\(-4x + 4\) |
Add \(4^x\) to both quantities to get:
Quote:
Quantity A |
Quantity B |
\(5x - 6\) |
\(4\) |
Add 6 to both quantities to get:
Quote:
Quantity A |
Quantity B |
\(5x \) |
\(10\) |
Divide both quantities by 5 to get:
Quote:
Quantity A |
Quantity B |
\(x \) |
\(2\) |
Since we’re told \(x > 2\), the correct answer is A.
The main/only drawback with this strategy is that you need to be careful when dividing and multiplying variables that may or may not be negative.
gmatclubot
GRE Matching Operations A powerful QCQ strategy [#permalink]
21 Jan 2022, 10:45
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