The most difficult GMAT Quant questions often have nothing to do with setting up equations for triangles or finding how many different arrangements you can make of a group of people standing in a line. Often, the most difficult GMAT Quant question in a seemingly innocuous form:
Is x an integer? Is b even? Which of the following must be positive?
Integers seem so harmless! But within the broad scope of integers, let’s look at a few key concepts about integers that you’ll need to know to beat the GMAT:
1) Integers are whole numbers: positive, negative, or zero. They belong to the set {… -3, -2, -1, 0, 1, 2, 3 …}.
2) When an integer is added, subtracted, or multiplied by another integer, the result is ALWAYS another integer. This note will come in handy particularly when looking at Data Sufficiency questions. Knowing that a result is always something allows you to answer a Data sufficiency question with an unequivocal “yes” or “no”.
3) Zero is neither positive nor negative. It has no sign + or – sign. All integers other than zero are either positive or negative.
4) Zero IS an even integer. Any integer divisible by 2 is considered an even integer. Zero divides into 2 with no remainder; therefore, zero is an even integer. Integers with the last digit of 0, 2, 4, 6, or 8 are all even integers. Conversely, integers with the last digit of 1, 3, 5, 7, or 9 are odd integers.
Though all of the concepts above may seem rudimentary, keep in mind the following: for all integers other than zero, an integer will have BOTH properties: positive vs. negative and odd vs. even. Let’s say that set A contains 5 distinct even integers, and set B contains 5 distinct negative integers. Too often, a test-taker will say “set A is {2, 4, 6, 8, and 10}, and none of those are negative” and think that the two sets cannot have any intersection. But it’s very possible to have sets A and B to contain the exact same integers. Both sets could have {-2, -4, -6, -8, and -10}.
If you see a question asking you “Is so-and-so an integer?” keep in mind the different properties of integers listed above so that you can answer the question as quickly as possible (while of course, still answering it correctly!). This is the type of basic, yet potentially troublesome, math content that is crucial for test day, and is included extensively in the math content review in the newly updated Kaplan GMAT course for 2010. Be sure that your test preparation materials have a thorough basis for reviewing math content and providing those crucial test-day tips and most-tested math theorems and facts! Best of luck!
