AIJobalert.comSarkari Naukri • Behtar Bhavishya

Get Free Job Alerts Request a Job Update

AIJobalert.comSarkari Naukri • Behtar Bhavishya

Number System Concepts and Exam-Oriented Problem Solving

This lecture covers core Number System concepts frequently tested in competitive exams, including midpoint number identification, sum and difference relations, LCM-based remainder problems, fraction manipulation, and prime numbers. The instructor explains multiple solution methods for each type, contrasting algebraic equations with short-cut formulas and option elimination techniques.

Railway
SSC
Maths
English
· 6 topics
Checked against the video on 19 Oct 2026

Made by AI from the YouTube video Complete Number System by Ajay Sir | Number System For UPP, Railway, SSC CGL, CHSL, MTS etc (opens YouTube in a new tab) by SSC MAKER, then checked against it. All credit for the teaching goes to the creator. Tap a topic’s time to confirm a fact in the video.

Number System Concepts and Exam-Oriented Problem Solving

EnglishWatch the video (opens YouTube in a new tab)

Checked against the video

This lecture covers core Number System concepts frequently tested in competitive exams, including midpoint number identification, sum and difference relations, LCM-based remainder problems, fraction manipulation, and prime numbers. The instructor explains multiple solution methods for each type, contrasting algebraic equations with short-cut formulas and option elimination techniques.

Equidistant Number Between Two Values

A number that is as much greater than one value as it is less than another is simply the arithmetic mean (midpoint) of the two values.
Must knowIf a number is as much greater than x as it is less than y, the required number is calculated using the formula (x + y) / 2.
The standard algebraic method sets up the equation x - a = b - x, which resolves to 2x = a + b.
For the problem where a number is as much greater than 31 as it is less than 75, the calculation is (31 + 75) / 2 = 106 / 2 = 53.
In a similar worked example, the number equally distant between 49 and 95 is (49 + 95) / 2 = 144 / 2 = 72.
For 39 and 79, the midpoint number is calculated as (39 + 79) / 2 = 118 / 2 = 59.

Product of Two Numbers from Sum and Difference

When the sum (x + y) and the difference (x - y) of two numbers are known, the individual numbers can be found by adding and subtracting the two simultaneous equations.
In the given problem, the sum of two numbers is 75 (x + y = 75) and their difference is 25 (x - y = 25).
Must knowAdding the equations gives 2x = 100, which results in the larger number x = 50.
Substituting x = 50 into the sum equation gives 50 + y = 75, resulting in the smaller number y = 25.
The product of the two numbers is calculated as x × y = 50 × 25 = 1250.

Largest Multi-Digit Numbers with Divisibility and Remainders

To find numbers that leave a constant remainder when divided by multiple divisors, first determine the Least Common Multiple (LCM) of the divisors.
For two divisors 6 and 5, their LCM is 30.
To find the largest two-digit number leaving a remainder of 1 when divided by 6 and 5, take the highest multiple of 30 below 100 (which is 90) and add the remainder: 90 + 1 = 91.
Option elimination also verifies that 91 divided by 6 leaves remainder 1 (6 × 15 = 90, remainder 1) and divided by 5 leaves remainder 1 (5 × 18 = 90, remainder 1).
Must knowTo find the largest three-digit number leaving remainder 3 when divided by 4 and 5, first find LCM(4, 5) = 20.
Dividing the largest three-digit number (999) by 20 gives a quotient of 49 and a remainder of 19; subtracting 19 from 999 gives 980, the largest three-digit multiple of 20.
Adding the required remainder 3 to 980 gives the final answer: 980 + 3 = 983.

Common Difference Remainder Problems

In problems where divisors and their respective remainders have a constant difference (Divisor - Remainder = k), the required number is given by a multiple of LCM minus k.
For divisors 6 and 7 leaving remainders 3 and 4, the difference is constant: 6 - 3 = 3 and 7 - 4 = 3, so k = 3.
The LCM of 6 and 7 is 42, and the largest two-digit multiple of 42 is 42 × 2 = 84.
Must knowSubtracting the common difference k = 3 from 84 gives the largest two-digit number: 84 - 3 = 81.
In another problem with divisors 7 and 11 leaving remainders 3 and 7, the common difference is 7 - 3 = 4 and 11 - 7 = 4, so k = 4.
The LCM of 7 and 11 is 77, and the smallest such number is LCM - k = 77 - 4 = 73.

Fraction Problems and Option Elimination

Problems involving algebraic operations on the numerator and denominator of a fraction are fastest solved using the option elimination method.
Given condition 1: adding 2 to both numerator and denominator yields 9/11; condition 2: adding 3 to both yields 5/6.
Testing option 7/9: adding 2 gives (7 + 2)/(9 + 2) = 9/11 (satisfies condition 1).
Testing condition 2 on 7/9: adding 3 gives (7 + 3)/(9 + 3) = 10/12, which simplifies to 5/6 (satisfies condition 2), confirming 7/9 is the correct fraction.
Must knowFor a fraction where the numerator is 4 less than the denominator, testing 3/7 shows a difference of 7 - 3 = 4.
Reducing its numerator by 2 and increasing its denominator by 1 gives (3 - 2)/(7 + 1) = 1/8, where the denominator 8 is exactly 8 times the numerator 1, confirming the fraction is 3/7.

Telescoping Series, Primes, and Successive Division

A telescoping sum of unit fractions whose denominators factor into n*(n+1) can be decomposed into partial fractions: 1/(n*(n+1)) = 1/n - 1/(n+1).
The expression 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 decomposes into (1/4 - 1/5) + (1/5 - 1/6) + ... + (1/9 - 1/10).
All intermediate terms cancel out, leaving First Term - Last Term: 1/4 - 1/10 = (5 - 2)/20 = 3/20.
Must knowThe largest two-digit prime number is 97, because 99 is divisible by 3 and 11, 93 is divisible by 3 and 31, and 91 is divisible by 7 and 13.
When a number divided by 192 leaves a remainder of 54, the remainder when the same number is divided by 16 is found by dividing the first remainder by 16 (since 192 is completely divisible by 16).
Must knowDividing 54 by 16 gives 16 × 3 = 48 with a remainder of 54 - 48 = 6.

Key terms

Equidistant Number: The number located exactly midway between two given values, calculated as their average.
Prime Number: A number greater than 1 that has no positive divisors other than 1 and itself.
Telescoping Series: A series where consecutive intermediate terms cancel out, leaving only the first and last components.
Partial Fraction Decomposition: Breaking down a complex fraction into a sum or difference of simpler fractions.

Formulas

Midpoint Number = (x + y) / 2: Used to find a number equally distant between two values x and y
Number = LCM(Divisors) × m - k: Used when divisors and remainders have a constant difference k = Divisor - Remainder
1 / (n × (n + 1)) = (1 / n) - (1 / (n + 1)): Used to split terms in a telescoping fraction series

Exam tips

When the original divisor is a multiple of the new divisor, simply divide the original remainder by the new divisor to get the new remainder.

Quick revision

The number equally distant between 31 and 75 is 53.
The number equally distant between 49 and 95 is 72.
If the sum of two numbers is 75 and their difference is 25, the numbers are 50 and 25, and their product is 1250.
The largest two-digit number giving remainder 1 when divided by 6 and 5 is 91.
The largest three-digit number giving remainder 3 when divided by 4 and 5 is 983.
The largest two-digit number giving remainders 3 and 4 when divided by 6 and 7 is 81.
The smallest number giving remainders 3 and 7 when divided by 7 and 11 is 73.
The sum 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 simplifies to 3/20.
97 is the largest two-digit prime number.
If dividing a number by 192 yields a remainder of 54, dividing it by 16 yields a remainder of 6.

These notes are made by AI from the video. Use the timestamps to check any important fact against the video before you rely on it.

Have a lecture of your own? Paste the YouTube link and get notes, a quiz and flashcards.

Make notes from a YouTube video

Browse every checked set of notes, filed by exam and subject.

Open the notes library

Made this video? Remove these notes

Open the Railway folder →

Number System: Classification of Numbers and Real Number Operations
This lecture covers the hierarchical classification of numbers from complex to natural numbers. It focuses on distinguishing rational and irrational numbers using decimal expansion, square roots, and algebraic operations, accompanied by solved exam questions.
Maths
English
6 topics
19 Oct 2026
By Maths WIZARD Aditya Ranjan
SSC
Railway
Banking
अनुपात और समानुपात (Ratio and Proportion) - SSC GD मास्टर क्लास
इस व्याख्यान में धर्मेंद्र डागर सर द्वारा अनुपात एवं समानुपात के मूलभूत नियम, अनुपात की तुलना और संयोजित अनुपात सिखाए गए हैं। इसके अंतर्गत प्रथम, मध्य, तृतीय और चतुर्थ समानुपाती की अवधारणाओं तथा उनसे संबंधित विगत वर्षों के प्रश्नों को हल किया गया है।
Maths
हिन्दी
7 topics
18 Oct 2026
By Rojgar with Ankit
SSC
Class 10 Mathematics Activity Book Solutions: Arithmetic Progressions and Coordinate Geometry
Solved activity workbook pages for Class 10 Mathematics covering patterns, arithmetic progressions, and coordinate geometry formulas. Includes determination of terms, common differences, sums of series, distance formula, midpoint formula, and centroid of triangles.
Maths
English
3 topics
18 Oct 2026
By Avinash Nandyal
Class 10 Mathematics: Real Numbers, Pair of Linear Equations, and AP Activities
Practical solved activities covering prime factorisation, HCF, LCM, and irrational number proofs. Includes graphical solutions and consistency conditions for pairs of linear equations in two variables. Concludes with an introduction to arithmetic progressions using toothpick patterns.
Maths
English
8 topics
18 Oct 2026
By ವಿದ್ಯಾಲಯ
Indefinite Integration JEE Brief
This lecture covers core concepts and problem-solving techniques for indefinite integration targeted at JEE Mains and Advanced. Topics include standard formulas, algebraic substitutions, integration by parts (ILATE rule and DI shortcut), standard quadratic forms, and partial fractions.
Maths
English
8 topics
18 Oct 2026
By Vora Classes