PYQ practice ka best order kya hona chahiye?

Pehle HCF-LCM + divisibility, phir remainders & modulo, then unit digit/last two digits, factorial (zeros & highest power), and last me digits/series patterns.

Unit digit PYQ fast kaise solve karein?

Base ka last digit lo, cycle length (1/2/4) use karo, exponent mod cycle karke position pick karo.

Factorial trailing zeros PYQ fast trick?

Trailing zeros = v5(n!) = floor(n/5)+floor(n/25)+floor(n/125)+...

21. Previous Year Questions (Number System) – SSC CGL

SSC CGL Number System previous year questions (PYQ) practice: HCF-LCM, remainders, unit digit, factorial zeros, digits, divisibility & patterns. Solutions with short tricks + answer keys.

← Prev: Series & Patterns Next: Practice Questions →

PYQ Set (SSC CGL style) – Questions

Note: Ye questions SSC level ke typical PYQ pattern par based hain (same concept coverage). Aap chahein to main “year/shift” wise exact PYQ mapping bhi add kar dunga.

HCF-LCM: Find LCM of 24, 36 and 54.
HCF: Find HCF of 96 and 128.
Remainder: Find remainder when 7¹⁰³ is divided by 10.
Unit digit: Unit digit of 3⁹⁹⁹?
Last two digits: Find last two digits of 7²⁰².
Factorial zeros: Number of trailing zeros in 100!?
Highest power (Legendre): Highest power of 2 in 50!?
Divisibility: Smallest number which when divided by 12, 15, 18 leaves remainder 5 each time.
Digits: Using digits 0,1,2,3 how many 3-digit numbers can be formed without repetition?
Prime/Composite: How many prime numbers are there between 1 and 50?
HCF word: Ropes 84 m and 126 m cut into equal max pieces. Length?
Series: 2, 5, 10, 17, 26, ?

Show Solutions / Answer Key

1) LCM(24,36,54)

24=2³×3, 36=2²×3², 54=2×3³ ⇒ LCM=2³×3³=8×27=216

2) HCF(96,128)

96=2⁵×3, 128=2⁷ ⇒ HCF=2⁵=32

3) Remainder of 7¹⁰³ ÷ 10

Unit digit cycle of 7: 7,9,3,1 (L=4), 103 mod 4=3 ⇒ unit digit=3

4) Unit digit of 3⁹⁹⁹

3 cycle: 3,9,7,1 (L=4), 999 mod 4=3 ⇒ 7

5) Last two digits of 7²⁰²

7²=49, 7⁴ ends with 01 ⇒ 7²⁰²=7^4×50+2 ends with 49 ⇒ 49

6) Trailing zeros in 100!

v5(100!)=⌊100/5⌋+⌊100/25⌋=20+4=24

7) Highest power of 2 in 50!

v2(50!)=⌊50/2⌋+⌊50/4⌋+⌊50/8⌋+⌊50/16⌋+⌊50/32⌋=25+12+6+3+1=47

8) Smallest N such that N≡5 (mod 12,15,18)

N−5 divisible by 12,15,18 ⇒ N−5 = LCM(12,15,18)=180 ⇒ N=185

9) Digits 0,1,2,3 se 3-digit numbers (no repetition)

Total 4P3=24; invalid leading 0: 0 fixed then 3P2=6 ⇒ valid=24−6=18

10) Prime numbers between 1 and 50

Primes: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47 ⇒ total 15

11) Rope pieces (HCF)

HCF(84,126)=42 ⇒ length=42 m

12) Series 2,5,10,17,26, ?

Differences: +3,+5,+7,+9 ⇒ next +11 ⇒ 26+11=37

Quick revision (PYQ focus)

Remainder / unit digit ⇒ cyclicity mod 10
Trailing zeros ⇒ v5(n!)
Smallest number with same remainder ⇒ LCM based
Digits counting ⇒ leading zero rule

← Prev Next →