The video below introduces you the how Integers are used on the GMAT Test.
Integers in the GMAT Test [Transcript]
In this lesson, we will examine a systematic technique for drawing conclusions about expressions involving even and odd numbers. To demonstrate this technique, we’ll solve a question you saw earlier. Now in this question, we must determine whether x is even, and the two statements involve expressions that evaluate to be odd numbers.
Let’s begin with statement one. It tells us that xy plus y is odd. Now this expression involves two variables, x and y. And each variable can be either odd or even. So there are several different cases to consider, x and y can both be odd, or x can be even and y can be odd, and so on. Now each of these cases will cause the expression, xy plus y, to evaluate to be either odd or even. To keep track of the different cases, we’ll use a table. And for each case, we will determine whether the expression evaluates to be odd or even.
So what are the possible cases here? Well, x and y can both be even, x can be even and y can be odd, x can be odd and y can be even. Or both variables can be odd. So there are four different cases to consider. Now let’s see what effect each case has on our expression xy plus y. So for the first case, we’ll replace the x’s and y’s with E to show that they are both even.
Now to evaluate this, we will apply our rules regarding even and odd numbers. So in the first case, we have an even number times an even number which is even. And then to this, we will add an even number which will result in an even number. So for the first case when x and y are both even, the expression xy plus y evaluates to be even.
For the next case, we will plug in E’s and O’s for the even and odd numbers. And when we apply our rules, we see that the expression evaluates to be an odd number. We will follow the same steps for the other two cases. So we now know the outcomes in each of the four cases. Now statement one tells us that the expression xy plus y, evaluates to be an odd number. When we examine our table, we see that there is only one case where the expression evaluates to be an odd number.
In this particular case, x is even and y is odd. Since we can now be certain that x must be even, we can answer our target question which means statement one is sufficient. Now some students may find it cumbersome to plug E’s and O’s into the expression and then apply these rules for each case. So another strategy is to plug actual numbers into the expression. For example, if x and y are both even, we can replace both variables with 2’s. When we do this, our expression evaluates to be 6 which is even.
Now it doesn’t matter which odd numbers and which even numbers you plug in. However, it’s a good idea to use small numbers to make your calculations easier. So for odd numbers, plugging in a 1 will make calculations easier. And for even numbers, 2 is a good number to use. Now using a 0 for even numbers, can make calculations even easier. However, the only drawback is that a 0 might get confused for an o which represents odd numbers. The important point here is to use small values when plugging in numbers.
All right. For the next case, we will plug in a 2 for the even number and a 1 for the odd number. When we do this our expression evaluates to be 3 which is odd. We can continue this method for the other two cases and when we do so, we see that our results in this table are the same as they were in the first table. Once again, only one case results in the expression evaluating to be an odd number. So we can be certain that x is even which means statement one is sufficient.
Okay, now on to statement two. We will use the same strategy to examine the four possible cases. So for the first case, we will plug in E’s to represent even numbers. Then by applying our rules, we can see that this expression evaluates to be an even number. Following the same steps, we can test the other three cases as well. Alternatively, we can plug even and odd numbers into our expression and then evaluate them to get identical results. We have now tested all possible cases.
Now statement two tells us that the expression 6x minus 3y evaluates to be an odd number. When we examine either of our tables, we see that there are two cases where the expression evaluates to be an odd number. In one case, x is even and in the other case x is odd. Since x can be either even or odd, statement two is not sufficient which means the answer here is A. As you can see, we now have a systematic technique for drawing conclusions about expressions involving even and odd numbers.
So when you encounter a question involving even and odd numbers, consider creating a table to test the various cases. If you use a table, you can let E’s and O’s represent even and odd numbers and then apply the following rules. Or you can plug even and odd numbers into the expression and then evaluate. Finally, once you have tested each case, you can draw conclusions based on the various outcomes.