USEFUL FORMULAE & CONCEPTS FOR QUANTITATIVE APTITUDE - An iQuanta Presentation

Sep 22, 2026

A structured set of mathematical shortcuts and core ideas for quantitative aptitude, covering number system basics, key divisibility rules, and properties of factors and co-prime numbers. It explains formulas for sums of natural numbers, even/odd series, squares, cubes, and includes rules for last digits and digit-sum tests for numbers like 3, 7, 9, and 11. It further introduces remainders, modulus interpretation, and remainder theorems including Wilson’s and Euler’s totient approach with examples.

LanguageEnglish

CategoryExam

FormatPDF

Pages59

Reading Time2 h 29 min

AccessFree to download

INDEX

Important points to remember

Divisibility rules

Divisibility rule for 3 and 9

Divisibility rule for 7 and 11

Divisibility rules of 6,12,14,15,18,etc.

Properties of factors and co-prime numbers

Remainders and Remainder Theorems

1.Wilson's Remainder Theorem

2.Euler's Totient Theorem

iQuantaBuilding Learning Netwom423000二T℃C=2C喝mmath盛手CAT4=TC 码 # USEFUL FORMULAE&CONCEPTS FOR QUANTITATIVE APTITUDE # An iQuanta Presentation # INDEX 1 Number System www.iQuanta.in NUMBER SYSTEM ## Important points to remember: 1.The product of 'n’consecutive natural numbers is always divisible by n! 2.Square of any natural number can be written in the form of 3n or 3n+1. 3.Square of a natural number can only end in 0,1,4,5,6 or 9.Second lastdigit of a square of a natural number is always even except when last digit is ### 6.If the last digit is 5,second last digit has to be 2. 4.Any prime number greater than 3 can be written as 6k+1 or 6k-1. 5.Any two-digit number 'mn'can effectively be written as 10m+n and a three-digit number Imn'can effectively be written as 1001+10m+n. 6.Sum of 1st n natural number,1+2+3+….+n =∑n =n(n+1)/2 7.Sum of 1st n positive even numbers,2+4+6-------+2n =n(n+1) 8.Sum of 1st n positive odd numbers,1+3+5+------(2n-1)=n² 9.Sum of squares of 1st n natural numbers:12+22+32+-----n²=n(n+1)(2n+1)/6 10.Sum of cubes of 1st n natural numbers:13+2³+33+--------n³=(∑n)²=[n(n+1)/2]2 11.0 and 1 are neither composite nor prime. 12.There are 25 prime numbers less than 100. 13.There are 15 prime numbers less than 50. Adarsh Khandelwal,CAT 99.93%ler fromiQuanta shares gratitude Adarsh Khandelwal 21 December at 22:44·母 "Ups and downs in life are very important to keep us goingbecause a straight line even in an ECGmeans we are not alive."-Ratan Tata.A quote very close to my heart. From scoring 99.90%ile in JEE Main to being diagnosed with a chronic health problem and notbeing able to take JEE Advanced and being ill for about 4 years,due to which I had to take up adistance-learnng course from IGNOU and graduated as BA(Pol Science)in 2019 along withbattling my disease up till September 2021 and finally winning.But I always knew that "Apna timeaayega".Fast forward to June 2022,though not able to get into IITs,I started paving way for myultimate goal of getting into IIMs and took a challenge from my brother to crack CAT 2022 with apercentile greater than that of JEE Main's (so yay!). I started looking for the best coaching out there and stumbled upon a Quora article that directedme towards iQuanta.I enrolled in CAT 2022 Batch 2,at this point 1 must mention that at first I wasa bit skeptical about iQuanta and thought that how can any CAT coaching has a fee which is 25-30k less than some of the big names,but nevertheless I decided to buy it and I must say I wouldhave regretted not joining iQuanta.The dual pedagogy,24x7 doubt solving and peer-to-peerlearning helped me grow a lot in a very short time.I scored 99.93%ile and for that I would like tothank Jeet Singh,Abhishek Leela Pandey and Sajjan Barnwal for always being there and taking usthrough a truly awesome journey e. P.S.-Jeet Singh Sir,ab GDPI ki naao bhi paar lagwa dijiye 6?? | Section | | Section | | Section | | Total | | | --- | --- | --- | --- | --- | --- | --- | --- | | Verbal Ability &
Reading Comprehension | | Data Interpretation &
Logical Reasoning | | Quantitative Ability | | | | | Scaled
Score | Percentile | Scaled
Score | Percentile | Sealed
Score | Percentile | Overall
Scaled Score | Overall
Percentile | | 16.46 | 77.59 | 48.31 | 99.99 | 49.38 | 99.95 | 114.15 | 99.93 | For iQuanta CAT Course,Visit www.iQuanta.in ## Divisibility rules 2-when last digit of the number is 0,2,4,6,8. 4-when last two digits of the number is 00 or divisible by 4. 8-when the last three digits of the number is 000 or divisible by 8. 5-when last digit is O or 5. 2n-when last n digits of the numbers are divisible by 2n. 5n-when last n digits of the number are divisible by 5n. ### Divisibility rule for 3 and 9 3-Sum of the digits should be divisible by 3.9-Sum of digits should be divisible by 9. ### Divisibility rule fo

FAQs

What are the key divisibility rules for 2, 4, and 8?

A number is divisible by 2 if its last digit is even. It is divisible by 4 if the last two digits are 00 or divisible by 4, and divisible by 8 if the last three digits are 000 or divisible by 8.

How can you determine divisibility by 3, 9, 7, and 11?

Divisible by 3 when the sum of digits is divisible by 3; divisible by 9 when the digit sum is divisible by 9. Divisible by 7 when the difference between twice the unit digit and the remaining part is a multiple of 7 (or 0). Divisible by 11 when the difference between sums of alternate digits is 0 or divisible by 11.

What do remainder and modulus mean in the remainder theorem context?

Remainder is what remains after dividing a by a divisor, expressed as a = divisor × quotient + remainder. Modulus means remainder; thus a mod b equals the remainder obtained on dividing a by b.

Sep 22, 2026

Uploaded by Riley West