Number System Aptitude Tricks

Tricky questions on number system are enough to perplex even the best of minds let alone the anxious exam-takers. Starting from the number line itself, questions can range from the types of numbers, such as natural, whole numbers, etc to arithmetic and geometric progressions. Exams like the GRE, GMAT and many Indian entrance examinations do not necessarily test advanced mathematical concepts but are inclined more towards basic mathematical understanding within tight durations. Thus, making use of number system aptitude tricks will not just help you arrive at the right answer but will also save you time which is in short supply. So, we have brought to you this blog that aims to list down some of the major number system aptitude tricks that can assist you in doing quick calculations and thus ensuring time management for the quantitative section in your exam.

Also Read:

• Data Interpretation Tricks for GMAT/GRE
• Problems on Ages 

Number System Aptitude Tricks: Types of Numbers

Typically, these type of questions pertain to a certain classification of numbers. More often than not, this includes natural numbers, whole numbers, integers, rational numbers, odd & even numbers and prime & composite numbers. A few exams may also test on real, imaginary and complex numbers. To get a better idea of these number system aptitude tricks, take a look at the following illustration.

Whole numbers	0,1,2,3,4,5,6,7……
Natural Numbers	1,2,3,4,5,6,7,8,…….
Integers	………-3,-2,-1,0,1,2,3,4,5,6,………..
Prime Numbers	3,5,7,11,13,17,19,23……..
Co-Prime  Numbers	HCF = 1
Composite Numbers	4,6,8,9,12,14,15,16,18,20……..
Even Numbers	2,4,6,7,8,10,12,14……..
Odd Numbers	3,5,7,9,11,13,15………
Rational Numbers	In ‘p/q’ form wherein p & q are integers and q is not equal to 0
Irrational Numbers	Pi, e, √2, √3, √5, √7……………

Also Read: Number Series Questions for Competitive Exams

Number System Aptitude Tricks: Sums

Questions on finding the sums of sequences of numbers are rampant and you are likely to encounter one or two out of this category in whichever exam you are appearing for. These number system aptitude tricks for solving sums will come in handy while performing data interpretation.

Sum of the first n odd numbers:	n^2
Sum of first n even numbers	n(n+1)
Sum of the first n natural numbers	[n(n+1)]/2
Sum of the squares of the first n natural numbers	[n(n+1)(2n+1)]/6
Sum of the cubes of the first n natural numbers	[n(n+1)/2]^2

Divisibility Methods

Tricks of divisibility help you solve direct questions on numbers as well as indirect questions related to simplification, division, LCM and HCF amongst others. It is one of the most commonly utilised number system aptitude tricks and simply requires you to memorise the divisibility until at least 8 while the more you do, the better.

Divisibility by 2	Unit digit is 0,2,4,6 or 8
Divisibility by 3	Sum of the digits is divisible by 3
Divisibility by 4	Last two digits is divisible by 4
Divisibility by 5	Unit’s digit is either 0 or 5
Divisibility by 6	Divisible by both 2 & 3
Divisibility by 8	Last three digits is also divisible by 8
Divisibility by 9	Sum of digits is divisible by 9
Divisibility by 10	Unit digit is 0
Divisibility by 11	Difference of the sum of digits at odd places and the sum of the digits at even places is either 0 or perfectly divisible by 11
Divisibility by 12	Divisible by both 3 & 4
Divisibility by 14	Divisible by both 2 & 7

Number System Aptitude Tricks: A Few Bonuses

Other than the above-mentioned ones, here is a list of some more number system aptitude tricks that can help you crack quants questions efficiently. 

Find Percentage Faster

There are various number system aptitude tricks you can utilise for faster percentage calculations. Break down percentages and then add the resultant numbers. For example, to calculate 15%, break it down into 10% and 5%, calculate their percentages and then add the resultant numbers. 

Example: To calculate 15% of 450, find 10% which is equal to 45 and 5%  which is equal to 22.5, therefore 15% of 450 becomes 67.5 There you go.

Faster Large Number Multiplication {only when one of the numbers is even}

Divide the first number by 2 and then multiply the second number by 2. Lastly, multiply the resulting numbers and you will have your answer. This is one of the most useful number system aptitude tricks for quicker multiplications especially when you get larger digits.

Example: To calculate 18*230, divide 18 by 2 which comes out to 9 and double the second number which in this case becomes 460. Multiplying 9*460 becomes 4140 and this is your answer.

Square a two-digit number ending with 5

In this method, multiply the digit in the first place with its successor and then put 25 in the end.

Example: Let’s find 45^2

4*(4+1)=20

Now, fixing 25 at the end of 20 comes to 2025 which is your answer.

Using number system aptitude tricks can help you save those few extra minutes but they cannot act as substitutes for proper preparation. If you are planning to appear for any competitive exam, take the assistance of experts at Leverage Edu and build your own personalised plan so that you can sail through it with flying colors.