The GRE is the most widely accepted graduate admission test worldwide. The test measures verbal reasoning, quantitative reasoning and analytical writing skills of students. It is very important to know the content tested before we appear for the test. The quantitative reasoning section tests high school Math. The section is divided into four parts: Arithmetic, Algebra, Geometry and Data Interpretation. The section consists of four types of questions: Quantitative Comparison, Multiple-choice – Select One, Multiple-choice – Select One or More and Numeric Entry.

In this article, we will discuss one of the major area tested on the GRE quantitative section – Arithmetic. Arithmetic contributes to almost fifty percent of the quantitative section. So, without knowing the basics of Arithmetic no one can expect a respectable score on the GRE Quantitative Reasoning section. The concepts tested on Arithmetic are:

- Properties and types of Integers;
- Exponents and Roots
- Percentage and Percent Change
- Ratio and Proportion
- Rate and Work
- Properties of Decimals
- Properties of Fractions
- Sets
- Counting Methods
- Probability
- Real numbers

Generally, the arithmetic questions are characterized by dense information. So, it is very important to know how to organize the data given and the questions. We need to approach these questions in bite sized pieces. Now let’s see the concepts tested on each topic.

**Properties of Integers:**It includes concepts such as

**Divisibility: –** If x/y = Integer, x and y are integers where y ≠ 0, then y is a divisor (factor) of x provided. In this case, x is also said to be divisible by y. For example, 10/5 = 2(Integer), so 10 is divisible by 5.

**Remainders: –** If we divide a by b and we get quotient as c and remainder as d then it follows a = b c + d. For example, when 13 is divided by 5, the quotient is 2 and the remainder is 3 since 13 = (5) (2) + 3.

**Even and Odd Integers: – **Any integer that is divisible by 2 is an even integer like, 0, 2, 4, 6… And Integers that are not divisible by 2 are odd integers like 1, 3, 5….

**Prime Number:** – A prime number is a positive integer that has exactly two different positive divisors, 1 and itself For example, 2, 3, 5, 7, 11, and 13 are some prime numbers.

**Prime Factorization:** – Every integer greater than 1 either is prime or can be uniquely expressed as a product of prime factors. For example, 28 = (2)(2)(7), 27 = (3)(3)(3), and 100 = (2)(2)(5)(5).

**Exponents and Roots:**– The exponent rules which are very generally tested are:

**Percentage and Percent Change:**Percentage is defined as anything out of 100.

This is a very important topic because it can be easily merged with other topics and has a wide range of applications. Apart from direct questions on percentage, you can also find the application of percentages such as Profit and Loss, percentages in word problems too. Almost one third of arithmetic questions involves use of percentages. So knowing the basic concept of percentages is vital to solve a variety of problems in GRE.

Basic concepts of percentage for GRE include:

- Basic percentage calculations
- Percentage Change concepts
- Successive percentage change concept

When the question tests percent increase or percent decrease then use the formula; % change = Difference/Original * 100. For % increase, use the smaller number as original and for %decrease use the greater number as original.

**Ratio and Proportion:**– Ratio is the comparison of two or more quantities. For example, ratio of 4 girls to 5 boys is written as 4/2 or 4:2.

Proportion is used when we compare two ratios like 20/100 = 10/x.**Rate and Work: –**Rate and work questions are commonplace on the GRE. In simple terms, rate can be defined as the quantity per unit time. The important topics of Rate are Time & Distance and Time & Work. Rates can be considered as the applications of Numbers, Ratios and Percentages but in reality it’s better to consider them as a separate part of Arithmetic because questions from these two areas usually involve multiple concepts and hence they require few tricks and approaches to better deal with them. Problems on Rate can be easily done by organizing the given information in a Rate chart.**Properties of Decimals: –**In the decimal system the position of the period or decimal point determines the place value of the digits. For example, the digits in the number 1024.593 have the following place values**:**1 is at thousands place, 0 is at hundreds place, 2 is at tens place, 4 is at units place, 5 is at tenth place, 9 is at hundredth place and 3 is at thousandth place. Representation of decimal into scientific form is also tested on the GRE. Like, 0.0002 can be represented as 2*10^{-4}. The knowledge of addition and subtraction of decimals, multiplication of decimals and division of decimals are also useful on the test

**Properties of Fractions**: – A fraction is in the form of a/b, where a is the numerator and b is the denominator. And the denominator of a fraction can never be zero, because a fraction with denominator zero is not defined. One should know how fractions can be compared in a faster way. The knowledge of addition and subtraction of fractions, multiplication of fractions and division of fractions will be handy on the GRE. Mixed fraction is another way of representing the fraction. For example, = 13/5.**Sets: –**A set is a collection of unique elements, such as {1, 2, 3}. However, {1, 1, 2} is not a set because it has duplicate elements (1, 1). The knowledge of equivalent set, subset, union of set, intersection of set, addition of sets, subtraction of sets are required on the test. Questions on group formula and Venn diagram are very common on the test.**Counting Methods: –**The concepts of permutations and combinations are also tested. For example,

In how many ways the letters of the word COUNTING can be arranged so that all the vowels are always together?

So, you should know some useful methods to count objects. The formula used for arranging objects (When order matters) is^{n}Pr = n!/(n-r)! and the formula used for selecting objects (When order doesn’t matter) is^{n}Cr = n!/r!(n-r)!.

**Probability: –**Probability is the chance of occurrence of an event. For example, if a coin is tossed 3 times then what is the probability of getting three heads in a row?

Here are some important formulae which are tested on the GRE:

P (A and B) = P (A) P (B)

P (A or B) = P (A) + P (B) – P (A and B)

P (E) = 1 – P ()

We could face questions on probability which involves counting methods also. Such questions are now very common on the GRE.

**Real Numbers: –**All numbers that can be represented on number line are called real numbers. For example, etc. GRE doesn’t test imaginary numbers such as etc. Some properties of real numbers which are generally tested are-

**a + b = b + a****a b=b a****(a + b) + c = a + (b + c)****(a b)c = a(b c)****a b + a c = a(b + c)****a + b and a b are positive if a and b are both positives****a + b is negative and a b is positive if a and b are both negatives****a b is negative if a is negative and b is positive****a b = 0 if either a = 0 or b = 0 or both a and b are 0.****|a + b|≤|a|+|b|**

So, students, all you need to focus is on basics and better organization of your scratch paper work to score better. Quantitative Reasoning for GRE is much simpler than your secondary and higher secondary mathematics and even the student with a non-math background can get a decent score by just focusing on the right material and learning the right approaches.

Our intention is to provide complete information on the Arithmetic content of the Quantitative section in GRE meanwhile keeping it crisp and simple. Hence go ahead and focus on the areas mentioned to boost your score.

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