Quantitative Comparisons? What’s that mean?
Let’s just put it right out there: the quantitative comparison question type is bizarre. If you’re just starting out, you’re probably thinking, What is this thing? Even if you’ve been studying for a while, unless you really like math, you probably feel a little uncomfortable whenever a QC question pops up on the screen.
Why? Because we all realize that we could completely mess up a QC question and still get to one of the 4 answer choices, clueless that we’ve messed up. It’s not like the questions with the 5 regular answers, where at least I know when I mess up because my answer isn’t in the answer choices!
What is QC?
The GRE isn’t really a math test. These kinds of tests are actually trying to test us on our executive reasoning skills “ that is, how well we make decisions and prioritize when faced with too many things to do in too short a length of time.
Quantitative Comparison questions test our ability to (quickly) analyze some information and figure out how to quantities compare to each other. Imagine your boss dumping a bunch of stuff on you and saying, Hey, our client wants to know whether Product A or Product B is better liked in the marketplace. Can you answer that question from this data? If so, which is it: A is better, B is better, or people think they’re about the same?
We do, of course, have to do some math “ and sometimes that math is quite annoying. We usually don’t, however, have to do as much as is necessary on the more normal quant questions.
How does QC work?
If you already feel comfortable with the basics of QC, you may want to skim or skip through this particular section of the article.
QC questions will always give us two columns labeled Quantity A and Quantity B. There also might be additional information up above the two columns; if so, this information is a given that we have to consider when evaluating the problem.
The overall question, every single time, is: which Quantity is bigger?
For example, we might see this:
Oliver is 4 years older than Sam
Quantity A Quantity B
Oliver’s age now Sam’s age in 5 years
Which Quantity is bigger? Can we tell? And is that answer always true? In this case, let’s say that Oliver is 10 today. If so, then Sam is 6 right now, using the information contained in our given. How old will Sam be in 5 years? He’ll be 11, or 1 year older than Oliver today. For at least this one example (Oliver = 10), then, Quantity B is bigger.
There are four possible answers. Can we eliminate any based on what we’ve found out so far?
(A) Quantity A is always bigger than quantity B.
(B) Quantity B is always bigger than quantity A.
(C) The two quantities are always equal.
(D) I can’t tell, or there isn’t an always one way relationship
Answer A can’t be right, because we’ve just found one example where B is bigger. Answer C can’t be right for the same reason. So we’re down to two possible answers: B and D.
So, will this relationship always be true? Will the quantity in column B always be bigger? Or are there other possibilities?
No matter how old Oliver is right now, Sam is always 4 years younger. In 5 years, then, Sam will always be 1 year older than Oliver is right now. Quantity B will always be bigger, so answer B is correct.
Here’s a shorter way to remember the four answer choices to the question Which one is bigger?
A: Quantity A always
B: Quantity B always
C: Equal always
D: None of the above
Notice the theme? The first three answers are always answers. If we don’t have an always situation, then the answer must be D.
Try another one
Here’s another problem to try; what answer do you get?
x2 “ 9 = 0
Quantity A Quantity B
3 x
We don’t have much to do for the two quantities; A gives us a plain value and B gives us a plain variable. Here we have to do some work with the given:
(x+3)(x-3) = 0
x = -3, x = 3
Alternatively, you could solve this way:
x2 = 9
x = +3 and x = -3
The two possible values for x are 3 and -3. If Quantity B is 3, then the two quantities are equal, and A and C can’t be the correct answers. If, on the other hand, Quantity B is -3, then Quantity A is bigger, and B can’t be the correct answer. Because we don’t have an always situation, the correct answer is D.
What’s my overall QC strategy?
A new question pops up on the screen. Now what?
(1) Write down ABCD (your answer grid)
(2) Read the problem. Write down any givens. If there’s any way to manipulate or simplify that information, do so.
(3) Look at the two statements; write them down in some form. Your real goal here is to figure out how to compare the information, not necessarily find some specific value for each one. (As we saw with the Oliver and Sam question, we still might be able to determine an always relationship even when we don’t know specific values for the quantities in question.)
There are lots of different strategies to tackle this comparison “ too many to list in one article, unfortunately “ but some ideas about what to do are below (just after we finish step 4 of our full process).
(4) Cross off answers as you can eliminate them; either pick when you get down to one, or guess and move on when you get stuck.
How to Compare Quantities:
First, notice anything that’s similar about the two quantities:
– Do they both contain the same variables or refer to the same item, or person, etc.?
– If the problem includes a given, is there a way to use that given to find a connection between the two quantities?
Next, try to simplify the quantities. If both are complex, see whether you can simplify them at the same time. You can perform the same manipulations to the two quantities as long as they are legal manipulations for inequalities:
– You can add or subtract the same quantity from both sides
– You can square both sides; you can also take the square root as long as you know both quantities are positive
– You can multiply or divide both sides by the same amount as long as you know that both are positive
For example:
Quantity A Quantity B
x2 “ 4x + 2 x2 “ 6x + 9
Both sides contain an x2 term; subtract it from both sides:
Quantity A Quantity B
“4x + 2 “6x + 9
We can also add 4x to both sides:
Quantity A Quantity B
2 “2x + 9
The simpler comparison becomes: Which is bigger, 2 or “2x + 9?
Well, let’s see. If x = 10, then Quantity B becomes -11, so Quantity A is bigger. Cross off answers B and C on your answer grid.
But there are no restrictions on the possible values of x. What if it’s negative? If x = -10, then Quantity B becomes 29, so Quantity B is bigger. Cross off answer A on your answer grid.
The correct answer is D.
Okay, these are weird. What can I do to get better?
An enormous amount, actually. This article barely scratches the surface of DS. There are all kinds of great strategies out there “ how to test numbers, how to prove answer D, how to use theory vs. real numbers, and so on. If you’re taking a class or using some kind of a test-prep book, then you should be getting this strategy as part of your regular program. If you’re not, then you should make sure to seek out Quant Comp strategies during your preparation; such strategies will change the game for you!
Here’s one article to get you started; browse our blog for more.
Finally, of course, you’ll have to learn a bunch of math. The above, though, should help you get started on this kind-of-bizarre question type in the first place!