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Integers, the topic has been found in school books too. Students have been introduced to integers for a long time back. The **GMAT** exam is quite famous for universal acceptance. Most of the MBA aspirants are GMAT preparers and the quant section of GMAT is a fearing factor to many. Students in this exam are either proficient in the verbal reasoning or quant section of GMAT. Students, majorly non-engineers are afraid about solving the **GMAT quant** despite rigorous practice. Coming to integers, this topic has been dealt with in this article to ensure smooth processing by the students.

As we mentioned that students mostly have learned about integers during their school days but those knowledge have mostly been cornered in the brain and they did not face the need to revive them anymore. All of a sudden the preparation of GMAT arrives and the preparation tips for GMAT come in handy.

Integers are all multiples of 1 in the simplest words. All the positive and negative values like -2 to 2, or whole numbers or their negative opposites, everything is an integer. The excluded values are fractions, decimals, which also targets pi.

Example= -3, -2, -1, 0, 1, 2, 3

It is to be noted that the patterns indicate that the set of integers will direct towards infinity in either direction as – every individual whole number and its consecutive negative is an integer. Here, another thing has to be noted and that is 0 is also an integer despite it not having any unique features.

Now when the students have perceived a slight idea of how integers are, we can get into the fact that how 0 and 1 are unique integers and have their own set of features different from the others. Also, the following rule must be considered as shortcuts to further solve the problems laid in the test. These will create an idea inside the head, as to how the question must be solved – add, or divide, or multiply, or subtract.

**Even integer- **when any number after divided by 2 results in an integer is called even integer like 0, 2, 4, 6, or 8.

**Odd integer – **when any integer is not divisible by 2, or the outcome of which is not divisible by 2, like 1, 3, 5, 7, or 9 – it is called odd integers.

**Both even and odd integer – **only integers have the power to be both even and odd because decimal places instantly rule out the divisibility factor by 1 or 2. So, if the student comes across any question in the test stating the number is both even and odd then they must understand that it is an integer.

**Addition and subtraction – **

Any integer, when added or deducted from an integer, gives out another integer –

2 + 3 = 5

2 – 3 = -1

**Negative and Positive – **

Rules to be followed while adding or deducting integers.

When adding any negative integer means deducting the positive.

4 + (-5) = 4-5 = -1

(- 4) + (- 5) = (- 4)-5 = -9

Deducting the negative integer is equivalent to adding the positive (because double negatives cancel out)

4– (−5) = 4 + 5 = 9

(−3) – (−4) = (−3) + 4= 1

**Odd and Even – **

Add or deduct two of the same sort of result in an even integer and adding and deducting odd and even results in an odd integer.

To explain it,

Odd + or – odd = even

5+7=12

Even + or – even = even

12–8=4

Odd + or – even = odd

8+3=11

8–3=5

To understand this let us first understand that multiplying an integer will result in an integer but that is not the case with the division. If we divide 3/5 then the result will be in a decimal or fraction, which in turn is not an integer.

It is by now understood that while multiplying or dividing numbers with a similar sign, the result is always positive. Whereas, while doing it with different signs, the result is always negative.

Therefore,

Negative × or / negative = positive

(−5)×(−5)=25

Negative × or / positive = negative

(−5)×5=(−25)

Positive × or / negative = negative

5×(−5)=(−25)

Positive × or / positive = positive

5×5=25

A multiple is a product that is derived by multiplying one number with the other. For instance, 20 is the multiple of 4 because it is also divisible by 4.

A divisor is positive integers which are multiplied together to create a multiple. For instance, 4, 5, 2, 10, 1 are all factors of 20. But 3 is not a factor of 20 because 3 cannot be multiplied with any other integer to receive 20.

So,

MultipleFactor = Integer

Firstly, 0 is an even integer or to make one understand – 2 goes into it 0 times.

Secondly, 0 is the only neither positive nor negative value. So, if the question asks for negative numbers do not include 0, but do include it in case of ‘non-negative’ or ‘non-positive’ numbers.

Thirdly, any number when added or deducted from that number is 0. For instance, m + 0 = m, m – 0 = m.

Fourthly, any number multiplied by 0 is 0. For instance, m x 0 = m

Lastly, o cannot be divided or m/o = undefined.

The concept of prime numbers is quite commonplace in **GMAT Arithmetic** and so it is found in certain questions. As we are aware by now, prime numbers are positive integers which are divided by itself and 1. Or to make it easier, prime numbers have two factors to be considered – 1 and itself. Now, 1 is not taken as prime because its only factor is itself. So, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 are the ones with only being even.

Now, when we are aware of most of the GMAT arithmetic part of integers, we can focus on it without any interruptions. Thorough practice will definitely lead one to score high marks in the GMAT quant section.

*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College

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