Quick, what’s bigger, A or B? Or, perhaps they’re both equal? Or, maybe you just can’t tell. If you’re beginning to prepare for the GRE, these are precisely the considerations you have to make on the famous quantitative comparison questions, which constitute a sizable chunk of the two quantitative sections of the GRE.
GRE: Quantitative Comparison: What is It?
There can be as many as 8 or 9 quantitative comparison questions on each of the two quantitative sections of the test. As this is almost half of all the quantitative questions on the exam, you definitely want to have some reliable strategies to tackle this unique question type. Unlike a standard multiple-choice problem-solving question, the quant comp question presents you with two columns, Quantity A and Quantity B. Sometimes there is some additional information that pertains to both quantities and is positioned in the center above the two columns.
GRE Quantitative Comparison Tip:
Memorize the Answer Choices
Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question.
- These four options will always be the same, so you should know them backwards and forwards.
- You should be especially wary of the fourth option, Choice D. Many GRE quantitative comparison questions are structured such that one quantity – at first glance – appears greater, but after further consideration, we realize that the answer depends on what kind of values we consider.
GRE Quantitative Comparison – Example 1:
x is a positive integer | ||
Quantity A | Quantity B | |
x | x^{2} |
At first glance, we might be tempted to say that Quantity B is bigger. Most students would consider a number such as 2 or 3. Clearly, 2^{2} > 2 or 3^{2} > 3. The especially savvy student will further recognize that the question stipulates that x is a positive integer, so fractions can be ruled out as well as negative numbers. But is there any positive integer x such that x^{2} is NOT greater than x? There sure is!
When x = 1, the 2 quantities are equal! Correct answer is D – cannot be determined.
GRE Quantitative Comparison Tip:
Plug In Numbers!
- Consider Obvious Number AND Weird Numbers
- As mentioned above and demonstrated in the example, we should always be ready for answer choice D. If you plug in two sets of values and get contradictory results as to which quantity is greater, then boom – automatically D!
- As in the above example, when x = 2, Quantity B is greater; when x = 1, the quantities are equal. Boom – correct answer is D!
- What are the Weird Numbers?
- Quick – pick a number.
- Most people respond with 3 or 7 or 153.
- Most people don’t say ½ or -17.
- Weird numbers are the ones we don’t think of immediately, and they are as follows:
- Negatives (Definitely useful with absolute values and odd exponents)
- Fractions (Also consider with exponents, for instance, (½ ) > (½)^{2})
- Zero
- One
- Extremes
- Quick – pick a number.
GRE Quantitative Comparison – Example 2:
a < b < c < d | ||
Quantity A | Quantity B | |
ab | cd |
Here, it’s easy to see how plugging in numbers, both obvious and weird, can help us to solve this question fairly quickly. If a, b, c, and d are positive integers, clearly Quantity B would be greater. If we consider some weird numbers, say, a = -20, b = -10, c = 0, and d = 1, then Quantity A is greater. Boom – Choice D!
GRE Quantitative Comparison Tip:
Simplify the Quantities and Treat as Equation
One of the ways the test makers can inject difficulty into a quant comp question is to make the two sides look as dissimilar as possible. Your job is to reveal the similarities by some algebraic or arithmetic manipulation. In other words, simplify as much as you can and then treat the two quantities as an equation!
GRE Quantitative Comparison – Example 3:
x > 0 | ||
Quantity A | Quantity B | |
x (x – 1) | x^{2} |
At first glance, it’s difficult to see what the two quantities have in common. A simple distribution of the x in Quantity A causes the two columns to appear more similar: x^{2 }– x on the left and x^{2} on the right. Now let’s equate the two sides: x^{2 }– x = x^{2} ; if we subtract x^{2} from both sides, we get -x on the left and 0 on the right. Because we are given that x > 0, -x must be less than zero, and thus Quantity B (0) is greater.
GRE Quantitative Comparison Tip:
If Neither Quantity Contains a Variable, Eliminate D!
This final tip is fairly obvious, but it is easily forgotten if you get lost in the details of question. No matter how complicated the numbers look on each side, if there are no variables, there MUST be a solution in which one side is greater or the two sides are equal.
GRE Quantitative Comparison – Example 4:
Quantity A | Quantity B | |
(74 + 92)^{2} | 74^{2} + 92^{2} |
It would not be too unreasonable to try to calculate this manually, especially because you are provided with a primitive calculator on the GRE. The point is, however, that you can automatically eliminate Choice D since there are no variables. Finally, beyond that, you can just think about the differences with your common factoring rules: how does (x + y)^{2} differ from x^{2} + y^{2}?
Remember, if you foil out (x + y)(x + y) in Quantity A, you get the middle term as follows: x^{2} + 2xy + y^{2}. Thus, Quantity A is greater.
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