Prepping for the GRE? By now, you should be familiar with Quantitative Comparison problems. You know the type – you are given two quantities, one in Column A and the other in Column B. You’re asked to compare the quantities.
Before taking the GRE, it’s imperative that you know the four answer choices, which never change. They are:
Choice (A): Quantity A is greater.
Choice (B): Quantity B is greater.
Choice (C): The two quantities are equal.
Choice (D): The relationship cannot be determined from the information given.
You’ve likely heard about the “plugging in” strategy for approaching various standardized test problems. Let’s look at this strategy in depth.
Know when to use it.
The plugging in strategy works well when one or both quantities contain algebraic expressions. Do not draw conclusions based on plugging in just one number! Consider the following numbers as you employ the plugging in strategy: 0, fractions between 0 and 1, numbers greater than 1, and negative numbers. A good set of possible numbers to choose from are -10, -1,- 1/2, 0, 1/2, 1, and 10. If you plug in two different values and arrive at contradictory conclusions, then the correct answer must be Choice (D).
Sometimes, the Quantitative Comparison will have a condition like x = 0. This will narrow down your plugging in possibilities, making the problem more manageable.
Let’s looks at some examples.
Notice the problem stipulates that x is a nonnegative number. In other words, x must be greater than or equal to 0. Let’s begin by plugging in x = 0.
x = 0
In this case, Quantity B is greater. We can immediately eliminate Choices (A) and (C). Now let’s plug in a number greater than 1, say x = 3.
x = 3
In this case, Quantity A is greater. Stop! Since the two cases yield contradictory results, we can conclude that the correct answer is Choice (D) – the relationship cannot be determined from the information given.
This problem is also a good candidate for the plugging in strategy. At first glance, we may think that Quantity B is greater. Seems reasonable. Let’s plug in a few values for x.
x = 3
If x = 3, then Quantity B is greater. We can eliminate Choices (A) and (C). Now let’s try x = 1.
x = 1
In this case, the two quantities are equal. Once again, since our two cases yield different results, the correct answer is Choice (D) – the relationship cannot be determined from the information given.
Let’s look at the same example, but tweaked a bit.
Now, the only values we need to consider are those between 0 and 1. Let’s start with x = 1/2.
x = 1/2
In this case, Quantity A is greater. We can eliminate Choices (B) and (C). Let’s test another value.
x = 1/5
Again, Quantity A is greater. At this point, it seems reasonable to conclude that Quantity A is greater for all values of x between 0 and 1. The correct answer is Choice (A).
Know the limitations.
When using the plugging in strategy, it is important to realize that unless we get contradictory results, making Choice (D) the correct answer, our results may be inconclusive. That’s why we need to plug in different types of numbers. Often, there are an infinite number of possible cases. Fear not – if we try many cases of different types of numbers, we can be reasonably comfortable that if the results are consistent, we are likely correct.
Know when to walk away.
Let’s look at one more example.
Let’s try plugging in different values to Quantity B and see what happens.
x = 0
In this case, Quantity B is greater than Quantity A. We can eliminate Choices (A) and (C). Let’s try a larger value for x.
x = 10
Without calculating the entire expression, it is clear the Quantity B is still greater than Quantity A. Let’s try a few negative numbers.
x = -1
x = -5
So it seems like a safe bet that the answer is Choice (B). But wait! When using the plugging in strategy, don’t forget about your algebra skills. The given trinomial looks familiar. In fact, the expression in Quantity B can be factored to (x-2)(x-2) = (x-2)^2. If x = 2, then Quantity B is 0, which is less than Quantity A. The correct answer is actually Choice (D). In this case, we would have been better off solving this problem algebraically. Lesson learned. The plugging in strategy can be super effective but it also has limitations.