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. In fact, many of the data sufficiency questions are themselves based on number properties. So, in the next few posts we are going to focus on this topic.
THE DEFAULT MODE
The very first challenge in this topic is to overcome 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. A number of questions in the quant section are in fact 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 end up saying that each statement alone is sufficient. But since the question does not put any constraint on the values of x, y and z, we should try both positive and negative numbers. And on taking y and z as negative, you would realize that even both statements combined are not sufficient to give a definitive answer.
So, a very important point to remember for GMAT quant is that whenever you are plugging in values of a “number”, you need to consider all categories of numbers. Some categories that are especially important 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
There are a number of concepts related to integers that 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 go on to discuss the remaining in the upcoming posts.
PRIME NUMBERS
Numbers that are divisible only by ‘1’ and the number itself are called prime. This means that prime numbers have only two factors, ‘1’ and the number. Numbers which 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 uptil 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 you are confident with number properties, your road to conquering the GMAT will become much smoother.