Number System Questions for SSC MTS

Types of Numbers

Numbers are classified into several types and exam often asks you to identify them. Natural numbers start from 1. Whole numbers start from 0. Integers include negative numbers too. Rational numbers can be written as p/q form. Irrational numbers cannot — like root 2 or pi. Prime numbers have exactly 2 factors: 1 and themselves. Composite numbers have more than 2 factors.

• Natural Numbers: 1, 2, 3, ... (no zero, no negative)
• Whole Numbers: 0, 1, 2, 3, ... (zero included)
• Integers: ...-2, -1, 0, 1, 2, ... (negatives included)
• Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 — memorize first 10
• 2 is the only even prime number — very commonly asked
• 1 is neither prime nor composite — another exam favourite

Divisibility Rules

Divisibility rules let you check if a number divides another without actual division. SSC MTS loves these as direct 10-second questions. The most tested are for 2, 3, 4, 5, 6, 8, 9, and 11. Learn them as shortcuts.

• Div by 2: last digit is even (0,2,4,6,8)
• Div by 3: sum of digits divisible by 3
• Div by 4: last TWO digits divisible by 4
• Div by 5: last digit is 0 or 5
• Div by 6: divisible by both 2 and 3
• Div by 8: last THREE digits divisible by 8
• Div by 9: sum of digits divisible by 9
• Div by 11: difference of (sum of odd-position digits) and (sum of even-position digits) = 0 or 11

Unit Digit (Last Digit of Powers)

Unit digit questions ask what is the last digit of a big power like 7 raised to 53 or 3 raised to 47. These are very common in MTS. The trick is: unit digits repeat in cycles. You only need the unit digit of the base and the power. Find the remainder when power is divided by the cycle length.

• Cycle of 1: 1,1,1,1 — always 1
• Cycle of 5: 5,5,5,5 — always 5
• Cycle of 6: 6,6,6,6 — always 6
• Cycle of 4 digits (2,3,7,8): unit digit repeats every 4 powers
• Cycle of 2 digits (4,9): unit digit repeats every 2 powers
• For base ending in 0: unit digit always 0

HCF and LCM Basics

HCF (Highest Common Factor) is the biggest number that divides all given numbers. LCM (Least Common Multiple) is the smallest number divisible by all given numbers. A very important relationship connects them. MTS asks both direct calculation and word problems involving tiles, bells, ropes.

• HCF is always less than or equal to the smallest number
• LCM is always greater than or equal to the largest number
• Product of two numbers = HCF x LCM (only for TWO numbers)
• HCF of fractions = HCF of numerators divided by LCM of denominators
• LCM of fractions = LCM of numerators divided by HCF of denominators

Remainders and Basic Number Properties

Remainder questions are very common. You may be asked: what is the remainder when a number is divided by another, or find the smallest number that gives a specific remainder. Also, properties like odd+odd=even, odd x even=even etc. show up in simple MCQs.

• Odd + Odd = Even, Even + Even = Even, Odd + Even = Odd
• Odd x Odd = Odd, Even x anything = Even
• Consecutive integers: sum of n consecutive integers starting from 1 = n(n+1)/2
• If a number N gives remainder R when divided by D, then N = D x quotient + R
• Smallest number divisible by D giving remainder R = D + R (if R is less than D)

• Forgetting that 1 is neither prime nor composite — this single fact is tested directly in MCQs very often
• Confusing divisibility by 4 (last two digits) with divisibility by 8 (last three digits) — many students reverse these
• Applying HCF x LCM = product formula to THREE numbers — this only works for exactly two numbers
• In unit digit cycles, when remainder is 0 after dividing power by cycle length, take the LAST term of the cycle, not the first — example: 2 to the power 8, remainder = 0, unit digit is 6 (4th term), not 2
• Mixing up HCF of fractions and LCM of fractions — students swap numerator and denominator rules

• Divisibility Shortcut Ladder: 2-Even, 3-Sum, 4-Last2, 5-Zero/Five, 6-Both2and3, 8-Last3, 9-SumNine, 11-Difference — remember as 2,3,4,5,6,8,9,11 going up a ladder
• For unit digit cycles remember DONZO: D=digits 2,3,7,8 have cycle of 4. O=others like 4,9 have cycle of 2. N=never changes for 0,1,5,6. ZO=Zero and One always end in themselves
• HCF x LCM trick: think H-L as High-Low, multiply the two numbers to get H times L — like two friends, their product is shared equally between their best-of and their least-of
• Prime numbers under 30: 2,3,5,7,11,13,17,19,23,29 — count them, there are exactly 10. Mnemonic: 2 Cats, 3 Sat, 5 Very Nicely, 7 Eleven, 13 Steps, 17 Into, 19 Twenty, 23 Nicer, 29 Cats (silly but sticky)

• SSC MTS sets Number System questions at moderate difficulty — no tricks beyond divisibility, unit digits, and basic HCF/LCM. You will rarely see complex remainder theorems here.
• Unit digit questions appear almost every year and take only 10-15 seconds if you know the cycles — never skip these, they are free marks
• Divisibility rule for 11 is the most tested rule in recent MTS papers — practice it with 4 to 5 digit numbers
• Word problems on HCF/LCM use real-life themes: bells ringing together, tiles fitting a floor, ropes cut into equal pieces — identify which to apply: same time or same size means HCF, combined event means LCM
• If a question gives a large number and asks which of the four options is divisible by some number, apply divisibility rules to options directly instead of calculating — saves 40-50 seconds