HERE YOU'LL FIND a sample GRE Quantitative Comparison question, along with a "QuickTip" and a detailed analysis of the question. The question is more difficult than average—about 40% of GRE test-testers would answer it correctly.

Here are the key "specs" for GRE Quantitative Comparison:

HOW MANY: 14 questions

WHERE: In the 45-minute Quantitative Ability section, interspersed with Problem Solving questions

FORMAT: Multiple-choice (you select one of 4 choices by clicking on an oval)

SKILLS TESTED: Your ability to reason quantitatively (list of specific areas covered)

DIRECTIONS: The following directions will appear on your screen—just before your first Quantitative Comparison question (and you can access them while tackling any Quantitative Comparison question by clicking on the HELP button).
 

Directions: Each question of this type consists of two quantities, one in Column A and one in Column B. Compare the two quantities and indicate: if the quantity in Column A is greater if the quantity in Column B is greater if the quantities are equal if the relationship cannot be determined from the information given In some questions, additional information pertaining to one or both of the quantities to be compared is centered above the two columns.   Any symbol appearing in both columns represents the same thing in one column as in the other.   All numbers used are real numbers.   To review these directions for subsequent questions of this type, click on HELP.

Notice that the following sample question includes centered information (above Column A and Column B) that applies to both of the quantities to be compared.
 

* b < a < -1*
Column A a2 - b2	Column B (3a + 3b)(2a - 2b)
The quantity in Column A is greater. The quantity in Column B is greater. The quantities are equal. The relationship cannot be determined from the ......information given.

QuickTip:

In handling GRE Quantitative Comparison questions, you can sometimes manipulate one or both expressions to reveal the comparison. In this question, try factoring both quantities. (The expression in Column A is one of the test-makers' favorites: the difference of two squares.)

Analysis

To reveal the comparison, first express Quantity A in its factored form:

(a + b)(a - b)

Notice the similarity between this expression and the one in Column B. Now factor out the constants (numbers) in Quantity B so that Quantity B more closely resembles Quantity A:

(3a + 3b)(2a - 2b) =

6(a + b)(a - b) =

6(a² - b²)

Now consider the centered information:

b < a < -1

In light of this information, (a² - b²) must be a negative number. Multiplying a negative number by 6 yields an even smaller number (to the left on the real number line). Therefore:

6(a² - b²) < a² - b²

Quantity A must be greater than Quantity B.

The first response is is the correct one.