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PRACTICE PROBLEMS For many students, GMAT number properties is one of the most daunting sections of the exam. But it doesn’t have to be that way. The GMAT number properties section is just like any other difficult section during a standardized test:it can be mastered. The key to mastering a standardized test is knowing how to take one. Remember the SAT or ACT back in High School? Learning how to the take those exams was crucial to a high score. Fortunately, those rules that you learned for those examinations still apply. Therefore, being prepared for the GMAT number properties portion is all about understanding and reviewing very basic math concepts in order to save time. Below is a review of very basic mathematical definitions:

## Integers

Integers are numbers sans a fractional part such as 3, 2, 1. A number like 2.25, which is a decimal, is not an integer. Integers can also be negative, such as -3,-2,-1 but do not have a fractional part as well. Positive integers are defined as being whole numbers. The 0 is also an integer but is considered to be positive or negative.

## Factors

Factors are considered to be numbers that divides equally into another number. For example the number 3 is a factor of 12 because 12/4=3. It is also a factor of 6 because 6/2=3 or 9 because 9/3=3.

## Primes

Prime numbers are whole numbers that only have two divisors, the actual number itself and one. For example, the number 7 is a prime number because its only two divisors are 7 and 1.

## Greatest Common Factor

The Greatest Common Factor or GCF for short is the largest number that divides two numbers evenly. In order to determine the Greatest Common Factor is by setting up a prime factorization of two numbers and comparing common factors. The largest common factor between the two numbers is the GCF.

## Least Common Multiple

To find the least common multiple, you perform a prime factorization in the same manner as one would do for the GCF. However, the least common multiple is the smallest number of a multiple of two numbers.

## Units Digits

Unit digits are the number to the right of the tens position. For example, the units digit for the number 364 is 4.

After reviewing basic topics such as the ones previously described, creating a study schedule with practice questions is a good way to see where your strengths and weaknesses are. Once, you know where your weaknesses are, study accordingly.

One of the hallmark points of confusion on the GMAT is the dreaded Yes/No Data Sufficiency question.  In a Value question, such as “What is the value of x?” the question of sufficiency is a familiar one: if you can solve for x, you have sufficiency.  But in a Yes/No question, especially when variables are involved, finding a solid answer can be a much cloudier process.

The best way to clear this fog is with a concrete example.  Let’s look at this Data Sufficiency question, along with its first statement:

Is x positive?

(1) x^2 > 1.

Is Statement (1) sufficient to answer the question?  Unless you have a comprehensive understanding of the underlying Number Properties at work here, your first reaction to this statement is likely to try out different numerical values for x, because working with real numbers instead of variables will be a much more comfortable place for most of us.  We are free to try out any value for x, but our first consideration in checking this statement should be that the number we pick is permissible, according to the statement.  If it is not, we can’t even consider the number as an example.

Is zero a permissible number to use here?  Well, if x = 0, then x^2 is also 0, and this statement tells us that x^2 has to be greater than 1.  You have to take the statements as true, so zero is NOT a number we can use here (not permissible).

How about x = 2?  That puts us into permissible territory, because 2^2 = 4, and 4 > 1.  But even that is only half the battle.  Now that we know x = 2 is a permissible example, we have to see what answer it yields to our original question, “Is x positive?”  Since 2 is a positive number, the answer here is “Yes.”

Now we have one example in the bank, and we know that, given the information in this statement, the answer to the question can be “Yes.”  But is that enough to declare sufficiency?  Unfortunately, it is not.  If this statement is sufficient to answer the question, it will give us an unequivocal Yes or No answer; we know now that the answer could be Yes, but could it also be No?

Well, if the answer could be No, then that would mean x could be negative or zero.  We’ve already seen that x can’t be zero (because it’s not permissible, remember?), so what about x being negative?  Let’s take the flip side of our other example and try x = -2.  It would certainly answer the question stem with a No, but is it permissible?

Remember, the statement mandates that x > 1.  Working a little calculation, (-2)^2 equals (-2)(-2), and since the product of two negative numbers is a positive number, x^2 = 4 when x = -2.  So our second example is permissible after all, and it answers the question “Is x positive?” with a resounding “No.” Since we have answered the question with a potential “Yes” (when x = 2) and a potential “No” (when x = -2), this statement is actually insufficient in the end; we require further information to determine whether or not x is positive.

As we see, it is absolutely necessary to remember what must be assumed as true (the statements) and what may or may not be true (the question stem) when Picking Numbers in these types of problems.  While this specific example is not as challenging as some, and you may have logically thought through it with number properties rules from the outset, this thought process is vital to learn for these types of questions, and will be most helpful with the most challenging questions, where you cannot gather the potential scenarios quickly at a glance without doing some scratch work.  Questions like this are exactly why we’ve kept such a close watch on the methods used in Data Sufficiency questions throughout the new GMAT revision.  When the Yes/No monster rears its ugly, convoluted head, never forget when picking numbers: First permissible, then Sufficient!

GMAT data sufficiency questions test your ability to analyze a quantitative problem and recognize which information is necessary to figure out the solution.  What a data sufficiency question does NOT test you on is your ability to calculate and number-crunch.  A simpler way of addressing this might be to ask yourself a question as you work through a data sufficiency problem: “Is this enough?”  Keep this in mind as you evaluate (and on test day, avoid) two specific common errors that test-takers make while taking the GMAT:

Mistake #1: Combining statements when unnecessary

This is done when a test-taker looks at both statements and says “Yes, if I have both pieces of information, then I can figure out the answer, so together the statements are sufficient.”  However, you must remember that you’re also asked if either statement ALONE is enough to answer the question.  Understanding the differences among all five answer choices in itself can be a boost to your quantitative score.  As you look at each individual statement, ask yourself, “is this enough?”  Once you can definitively answer yes or no, you are then closer to an answer to the data sufficiency problem.

Mistake #2: Over-calculating

Since you may not need to calculate an actual value for a data sufficiency question, you should avoid going into the calculation step unless absolutely necessary.  For example, if dealing with a statement like:

2x + 15 – 7x + 32 = -1

Instead of trying to plow through with the calculations as you might have to do in a problem-solving question, recognize that you have one variable in this equation (x), and that this is solvable.  So if this shows up in a data sufficiency question, the answer to the question “is this enough?” is yes, and again you are closer to solving your data sufficiency question.

Though data sufficiency questions look very abstract, there’s a hidden beauty involved in solving them.  Practice these while taking on the mindset of “is this enough?” to maximize your time-management ability for the GMAT.

If n is an integer, is n/15 an integer?

(1) 3n/15 is an integer.
(2) 8n/15 is an integer.

All trainees in a certain aviator training program must take both a written test and a flight test. If 70 percent of the trainees passed the written test, and 80 percent of the trainees passed the flight test, what percent of the trainees passed both tests?

(1) 10 percent of the trainees did not pass either test.
(2) 20 percent of the trainees passed only the flight test. To get started with a FREE 3-week walkthrough of how to study for the GMAT, please enter your email below. We respect your email privacy and will never give away, trade or sell your email address.