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GRE Quant : Arithmetic - I


Understanding basics is an important step towards achieving a great score in the Quantitative Reasoning section.

In this post, we cover the basics of the Arithmetic portion. Arithmetic is not just about performing the basic operations of multiplication, division, addition or subtraction. It includes concepts of number systems, divisibility, ratios, percent, proportions and so much more.

Today, we cover properties of numbers and divisibility rules. 
The remaining concepts will be posted in another part of Arithmetic section.

We have also added a practice question for each concept explained so as to provide a better clarity. The sample questions are in line with the question types that you will encounter in your actual GRE General Test.

To learn more about the question types in the QA section, you can refer to our post on Introduction to Quantitative Reasoning.  

NUMBER SYSTEMS
Prime Number:
If a number is divisible by 1 and by itself only then it is called a prime number. 2 is the only even prime number.
Example:
Which of the following numbers CAN be expressed as the product of two prime numbers?
πŸ”˜23
πŸ”˜36
πŸ”˜51
πŸ”˜28
πŸ”˜67
Answer: 51

Integers: 
An integer is a whole numbers which include zero, positive and negative numbers. These integers can be visualized on the number line. 
Example:


                                                            
Points A, B, C and D are on the number line above, and AB=CD=1/11 BC. What is the coordinate of B?
πŸ”˜32/156
πŸ”˜45/156
πŸ”˜57/156
πŸ”˜78/156
πŸ”˜2/156
Answer: 57/156

Decimal Number:  
A decimal number expressed with a decimal point in it. Like 3.4, 4.5 etc.
Example: 
X is the decimal form of 3/7.
            QUANTITY A         
        QUANTITY B                                   
 The 11th digit to the right of the decimal point of X.                 3
 
πŸ”˜Quantity A is greater
πŸ”˜Quantity B is greater
πŸ”˜The two quantities are equal
πŸ”˜The relationship cannot be determined from the information given.
Answer: Quantity A is greater.

Composite Numbers: 
A number which can be divided by a different number other than 1 and the number itself.

Whole Numbers: 
The set of numbers that include natural numbers and the number zero.
Example:
The integers x and y are greater than 1. If (7x)(8y)=840, what is the value of x+y ?
πŸ”˜5
πŸ”˜8
πŸ”˜12
πŸ”˜9
πŸ”˜15
Answer: 8

Rational Numbers: 
The numbers that can be expressed in the form of a/b where a and b are integers and b ≠ 0.
Example:
Which of the following operations carried out on both the numerator and the denominator of a fraction will NOT produce an equivalent fraction? Indicate all such operations.
πŸ”˜Subtracting 8
πŸ”˜Adding by 4
πŸ”˜Dividing by 456
Answer: Subtracting 8, Adding by 4

Irrational Numbers: 
The fractions that are non-terminating and non-recurring. For example: √2, e, Ο€ etc.

Highest Common Factor (HCF):
The highest of all common divisors to the numbers.
Example:
Which one of the following is the HCF of the following numbers: 198, 121, 1331 ?
πŸ”˜2
πŸ”˜4
πŸ”˜8
πŸ”˜10
πŸ”˜11
Answer: 11

Lowest Common Multiple (LCM):
The LCM of two numbers a and b is the smallest natural number that is divisible by both a and b.
Example:
What is the LCM of the following numbers: 462, 504, 594?
πŸ”˜16632
πŸ”˜14326
πŸ”˜18676
πŸ”˜12498
πŸ”˜20672
Answer: 16632

DIVISIBILITY
An integer is completely divided by the second number if and only if it is a multiple of the first number. The divisibility rules are as follows:
By 2: If the last digit of the number is divisible by 2. 
By 3: If the sum of the digits is a multiple of 3.
By 4: If the last two digits of the number is divisible by 4.
By 5: If the last digit of the number is 0 or 5.
By 6: If the number is divisible by both 2 and 3.
By 9: If the sum of the digits is a multiple of 9.
By 10: If the last digit is 0.
By 11: If the alternating sum of digits of the number is divisible by 11, then the number is divisible by 11.
 
Rules of Odd/Even Numbers
Odd + Odd = Even
Even + Even = Odd
Odd + Even = Odd
Odd × Odd = Odd
Even × Even = Even
Odd × Even = Even


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