An analysis of the quant section of GMAT brings out two striking points. First is the challenging question type of data sufficiency, something you might have come across for the first time and to which we devoted the previous two posts. The second is a clear emphasis on **number properties**. Many of the data sufficiency questions are themselves based on number properties. So, in the next few posts, we will focus on this topic.

**THE DEFAULT MODE**

The first challenge in this topic is overcoming the tendency to think of numbers only as counting numbers. Since many GMAT test takers have not been doing Math for a while, when they see the word “numbers,” they tend to think in terms of positive integers (1, 2, 3…) since these are the numbers we encounter most frequently in everyday life. Several questions in the quant section are designed to make you fall into this trap. Consider an example data sufficiency question

**1) **Is x > y

Statement #1: x = 3y

Statement #2: x = y+z

In this case, if you make the mistake of assuming that x, y, and z are positive integers, you would say that each statement alone is sufficient. However, since the question does not constrain the values of x, y, and z, we should try both positive and negative numbers. On taking y and z as negative, you would realize that combined statements are insufficient to give a definitive answer.

So, a very important point for GMAT quant is that whenever you are plugging in values of a “**number**,” you need to consider all categories of numbers. Some especially important categories are listed below.

a) 0

b) 1

c) Numbers between 0 and 1, and also between -1 and 0

d) Positive fractions (1/2, 3/5 etc.)

e) Negative fractions ( -2/5, -4/7 )

f) Negative integers (-1, -2, -3 etc.)

Remember that for a statement to be true, it has to be true for **all possible cases.**

Here is a question to help you practice considering all categories of numbers

**2) **If yz ≠ 0, is 0 < y < 1?

Statement #1: y < 1/y

Statement #2: y = z2

**MORE ABOUT INTEGERS**

Several concepts related to integers are frequently tested on the GMAT – prime composite, odd-even, factors and multiples, etc. Here, we shall discuss some important points about prime numbers and the remaining in the upcoming posts.

**PRIME NUMBERS**

Numbers that are divisible only by ‘1’ and the number itself is called prime. This means prime numbers have only two factors, ‘1’ and the number. Numbers that are not prime are called composite.

A few must-know points about prime numbers –

– ‘1’ is neither prime nor composite.

– ‘2’ is the only even prime number.

– There is no rule to predict prime numbers. You need to check divisibility by prime numbers until the square root of the number. E.g., to check the primality of ‘101’, we need to check divisibility up to 10.

– Only positive integers can be either prime or composite.

**Here’s a data-sufficiency question to help you get started with prime numbers**

**3) **Is x > y

Statement #1: x is prime, but y is composite

Statement #2: x is even

In the upcoming posts, we shall go into much greater detail about the applications of prime numbers for the GMAT. Once confident with **number properties**, your road to conquering the GMAT will become much smoother.

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