GRE Quantitative Comparisons Are Easier Than You Think

Another tip to keep in mind as you are doing quantitative comparisons is to compare rather than solve. The GRE is testing your ability to compare the quantities in the columns, NOT to do long calculations. In fact, it is a sure sign that you are doing the problem wrongly if you are doing complex calculations. Your goal should be to compare the columns.

One way to do this is to pay attention to the behavior of larger or smaller values. This means that the given columns may look very similar, but differ by a very minute aspect and your task will be to find out what that ultimately means as to which column is greater. Lets look at an example.

Notice these two columns are very similar. The only difference between them is the number in the denominator. While on the left we have 2 in the denominator, on the right we have something slightly larger 2.01. Now, if you saw this problem on test day, remember our tip: compare rather than calculate. It would be silly and time consuming to try to square the quantity in column B, but we know it is very similar to column A. If we have a slightly larger denominator, is the entire number slightly larger or slightly smaller?

Slightly smaller. Thus in column B we have a slightly smaller number being squared than column A. Thus Column B would end up being smaller when squared. So column A will always be bigger. Thus our answer is A.

This question required you to think about the behavior of numbers– what happens when a number is slightly bigger or smaller than a comparable value. Many quantitative comparisons test this, and that is why it is good to get in the habit of comparing rather than calculating.

In addition to paying attention to slight differences in the columns, it is helpful to simplify the columns as much as possible so that they look alike. This means that you use your arithmetic and algebra skills much like any other math problem, and consolidate the columns until you can compare them.

Lets say we have this as our quantitative comparison problem:

Now, initially it looks like the values would depend on what x and y are, so we would be tempted to choose D. But, if we simplify each column we may discover that we can compare them more accurately.

On the left hand side, if we remember our associative property rules, we know that we can simply drop the parentheses here and combine like terms. 3x and 5x gives us 8x, and we have a minus 5y.

On the right hand side, we need to be more careful with our parentheses, making sure to distribute the negative to each term of the parentheses. Thus we have 10x-7y-2x+2y. Combining like terms give us 8x minus 5 y.

So, lo and behold, they are exactly the same expression. Thus they are equal and our answer is C.

So you see that even if we can’t compare the columns initially, we can work with them until we can compare them. And of course, you will need to utilize your algebra and arithmetic skills here.

Another way to be able to compare the columns quickly and easily is to do the same thing to both columns. Many times, the columns cannot be directly compared unless you perform a mathematical operation on them to make them look similar.

Take this quantitative comparison question for example:

Now, to some viewers this may look daunting. For others, it may look simple. The key thing is to remember the tip of doing the same thing to both columns. Both columns have a radical: the cube root as their form. Thus, if we raised both columns to the third power, the cubed root radical would simply disappear, and our comparison would be much more simplified. So, lets do that. Cubing both sides, I am left with what was underneath the cube root sign.

We can then see that Column B is the product of two terms: the first term 3x, and the second term y squared minus 1. Perhaps we could get the same form in Column A? Let’s see how we do it:

Indeed, if we factor out an x from column A, we are left with x times y squared minus 1. This is very close to column B. Since they both have y squared minus 1, we can divide by them. Thus we have x for column A and 3x for column B. Now this is a much easier problem to handle!

At this point we do not want to divide by x because we need to consider the possible values of x. If x is negative, then column A would be larger, but if x is positive, column B is larger. Thus our answer is still D: not enough information to determine the relationship. This answer was much easier to arrive at once we simplified the problem. We did the same thing to both columns and factored until the columns were much more easily compared.

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Posted on 27. Dec, 2011 by Ryan in Math