GRE Arithmetic Practice Questions Types, Tips and Practice Papers

GRE Arithmetic is one of the four parts of the GRE Quantitative Reasoning. GRE Arithmetic includes various topics of integer properties, divisibility factorisations, exponents, roots, percents, ratios, and rates. GRE Arithmetic along with other parts in GRE Quant includes two subsections with 20 questions in each section. Candidates get 35 minutes for each section in GRE quant. The GRE score for quantitative reasoning stands at the range of 130-170.

GRE Arithmetic Question Types 

Being part of the GRE Quant, candidates would get similar GRE arithmetic question types within the four parts of the section. Candidates can follow the GRE exam pattern as part of their preparation for the test. These question types are as follows:

Quantitative Comparison: candidates will get questions in the form of word problems which they need to interpret in mathematical terms. It includes questions which have four potential answers. This includes quantity A is greater, quantity B is greater, both quantities are equal and their relationship cannot be determined.
Multiple Choice Questions: the questions in arithmetic GRE will be based on multiple choice. Candidates in some questions need to choose a single choice of answer while based on the instructions, choose multiple answers as well.
Numeric Entry: candidates need to insert the numericals like integers and decimals within a box. It also includes arithmetic and fractions GRE questions for which two separate boxes are given for filling fraction answers.

GRE Arithmetic Questions 

The arithmetic for GRE questions in the GRE Quant is based on different types of arithmetic concepts. The GRE arithmetic syllabus includes all these concepts which can be explained as follows with examples.

GRE Arithmetic Integers

Integers in arithmetic GRE are different types of numbers which are either positive or negative numbers. 0 is an exception because it is neither negative nor positive. The integers have their own features as follows:

• Addition of two integers will be an integer (negative or positive).
• Subtraction of two integers will be an integer (negative or positive).
• Product of two integers will be an integer (negative or positive).
• Division of two integers can be an integer or decimal (negative or positive).
• Square of an integer (negative or positive) will be a positive integer.
• Root of a positive integer can be an integer or decimal.

Example:

If an integer is divisible by both 12 and 27, then the integer must be divisible by which of the following?

(A) 48
(B) 54
(C) 81
(D) 108
(E) 324

Answer: (D)
Explanation: This question is really asking for the LCM of 12 and 27. First, get the prime factorizations of each number.
12= 22×3
27=33

GRE Arithmetic Decimals

The GRE arithmetic questions of decimals uses the decimal number system with a base of 10 where digits from 0-9 are used. Accordingly, the successive points from the left of the decimal is 10 etc and the successive points to the right are 10 and so on. Candidates can find books like Kaplan GRE Maths Guide for the purpose of GRE arithmetic practice.

Example:

GRE Arithmetic Exponents and Roots 

A number can be expressed in terms of base and its powers can be expressed as exponents. When a number is the form of  then it is expressed as the root of the number.

Example of base and exponents:

2. 125 = 
3. 1296 = 

Example of roots:

1.  = 

Example:

If √a=4 and ∛b=a, what is the value of b?

Answer: 4096
Explanation: √a=4 means “the square root of a number is 4.” You can guess and check, or better yet, translate the equation into: a=42, which is 16.

Then plug in a to the second equation: ∛b=16, and rewrite as: b = 163 = 4096.

GRE Arithmetic Percent 

Percent in arithmetic for GRE implies that a quantity or number which is per 100 quantity. Percent is denoted as %. For understanding how GRE arithmetic questions in percent is calculated an example is necessary:

Example question- If marks of the exam are less than 100. A student secured 35 marks out of 50 marks then what % of marks the student secured?

Answer-

= (Marks secured by student / Total marks of the exam) * 100
= % of marks student secured.
= (35 / 50) * 100
= (7 / 10) * 100
= 70%

GRE Arithmetic Fraction 

A number which is denoted in the form of a numerator/ denominator and the denominator is not equal to 0 is called a fraction. In arithmetic and fraction GRE questions, candidates need to understand it with an example. Accordingly, for the fraction 5/2, the numerator is 5 and the denominator is 2. Arithmetic operations of addition, subtraction, multiplication and division are possible in fractions.

Example:

GRE Arithmetic Ratio 

A ratio in arithmetic for GRE means that it is the measure of a quantity expressed for two or more entities. It is also expressed as a fraction with a numerator and denominator. Examples for ratio in the form of GRE arithmetic questions are as follows. The questions would help candidates to achieve a higher GRE score.

Example: In furniture shop the ratio of ‘chairs is to tables is to sofas’ is 5 is to 7 is to 10
or 5 : 7 : 10 What is the ratio of chairs to sofas?
Solution: The ratio of chairs to tables is 5 is to 7
or 5 : 7
or 5 / 7
The ratio of tables to sofas is 7 is to 10
or 7 : 10
or 7 / 10
i.e. there are 5 chairs for every 10 sofas
or 5 : 10
or 1 / 2

GRE Arithmetic Real Numbers 

Real numbers include the set of rational and irrational numbers. Integers, fractions, decimals are all part of the real numbers and the arithmetic GRE includes questions based on the real numbers. In a number line, all numbers negative and positive are real numbers.

Example:

8 + 2 = 2 + 8 = 10
(-3)(17) = (17)(-3) = -51