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22. Practice Questions (Mixed + Timed) – Number System

SSC CGL Number System mixed practice (timed set): HCF-LCM, divisibility, remainders, unit digit/last two digits, factorial (zeros & highest power), digits & series. Timer-friendly set with answers + quick solutions.

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Timed Set Instructions

Questions (Mixed) – Top 50 Most Important (SSC CGL Number System)

  1. Find HCF of 180 and 252.
  2. Find LCM of 18, 24 and 30.
  3. Smallest number which leaves remainder 3 when divided by 8, 12 and 20.
  4. Remainder when 345 is divided by 7.
  5. Unit digit of 7999.
  6. Last two digits of 1357.
  7. Trailing zeros in 250!.
  8. Highest power of 3 in 100!.
  9. How many 4-digit numbers can be formed using digits 0,1,2,3,4 without repetition?
  10. Smallest number formed using digits 0,0,2,5.
  11. If a 2-digit number is 27 more than its reverse, find the difference between its digits.
  12. Find number of primes between 1 and 100.
  13. Find the least number that must be added to 9876 to make it divisible by 11.
  14. Find remainder when 2100 + 3100 is divided by 5.
  15. Find last digit of 9123.
  16. If N is divisible by 12 and 18, then the smallest such N greater than 100?
  17. Find the smallest number which when divided by 6,7,8 leaves remainder 1 each time.
  18. How many trailing zeros in (50!)2?
  19. Find the missing term: 2, 5, 10, 17, 26, ?
  20. Find remainder when 99999 is divided by 9.
  21. Find HCF of 144, 180 and 252.
  22. Find LCM of 16, 20 and 24.
  23. LCM of two numbers is 420 and HCF is 21. If one number is 105, find the other number.
  24. HCF of two numbers is 12 and their product is 1728. Find their LCM.
  25. Three bells ring at intervals 12 min, 15 min and 18 min. If they ring together now, after how many minutes will they ring together again?
  26. Ropes of length 84 m and 126 m are cut into equal pieces of maximum length. Find the length of each piece.
  27. A floor of size 96 m × 120 m is to be tiled with largest square tiles. Find side of the tile.
  28. Least number which when divided by 7, 9, 12 leaves remainder 5 in each case.
  29. Remainder when 2103 is divided by 7.
  30. Remainder when 5123 is divided by 13.
  31. Remainder when 7222 is divided by 9.
  32. Find remainder when 1150 is divided by 12.
  33. Find remainder when 250 + 350 is divided by 7.
  34. Unit digit of 13202.
  35. Unit digit of 2999 + 3999.
  36. Last two digits of 3100.
  37. Last digit of 72025.
  38. How many trailing zeros in 1000!?
  39. How many trailing zeros in 125!?
  40. Highest power of 2 in 100!?
  41. Highest power of 5 in 500!?
  42. Highest power of 12 in 50!?
  43. Using digits 1,2,3,4,5 how many 3-digit numbers can be formed without repetition?
  44. Using digits 0,1,2,3,4 how many 5-digit numbers can be formed without repetition?
  45. Find the largest number using digits 0,2,2,5,7.
  46. Find the smallest number using digits 0,2,2,5,7.
  47. Find sum of all 3-digit numbers formed using digits 2,4,6 without repetition.
  48. Find the missing term: 1, 4, 9, 16, 25, ?
  49. Find the missing term: 7, 10, 15, 22, 31, ?
  50. Find the missing term: 3, 6, 12, 24, 48, ?
  51. Find the missing term: 1, 3, 6, 10, 15, ?
  52. Find the missing term: 2, 6, 18, 54, ?
Answer Key + Short Solutions (Top 50)
  1. 36 — HCF(180,252): 180=2²·3²·5, 252=2²·3²·7 ⇒ common = 2²·3²=36
  2. 360 — LCM(18,24,30)=2³·3²·5=360
  3. 123 — N≡3 (mod 8,12,20) ⇒ N−3 divisible by LCM(8,12,20)=120 ⇒ N=120+3
  4. 6 — 3⁶≡1 (mod7), 45≡3 (mod6) ⇒ 3⁴⁵≡3³=27≡6
  5. 3 — 7 cycle (7,9,3,1), 999 mod4=3 ⇒ unit digit = 3
  6. 33 — 13⁵⁷ (mod100): 13²=69, 13⁴=61, 13⁸=21, 13¹⁶=41, 13³²=81 ⇒ 57=32+16+8+1 ⇒ 81·41·21·13≡33
  7. 62 — zeros in 250! = ⌊250/5⌋+⌊250/25⌋+⌊250/125⌋ = 50+10+2
  8. 48 — v₃(100!)=⌊100/3⌋+⌊100/9⌋+⌊100/27⌋+⌊100/81⌋=33+11+3+1
  9. 96 — 5P4=120; leading 0 invalid: 0 fixed then 4P3=24 ⇒ 120−24
  10. 2005 — smallest with 0,0,2,5: first non-zero 2, then 0,0,5 ⇒ 2005
  11. 3 — (10a+b) − (10b+a)=9(a−b)=27 ⇒ a−b=3
  12. 25 — primes 1..100 = 25
  13. 2 — 9876 ÷11 remainder = 9 (since 11×898=9878) ⇒ add 2 to reach 9878
  14. 2 — mod5: 2⁴≡1 ⇒ 2¹⁰⁰≡1; 3⁴≡1 ⇒ 3¹⁰⁰≡1 ⇒ sum≡2
  15. 9 — 9 cycle (9,1), 123 odd ⇒ 9
  16. 108 — LCM(12,18)=36 ⇒ next multiple >100 is 108
  17. 169 — N≡1 (mod6,7,8) ⇒ N−1 divisible by LCM(6,7,8)=168 ⇒ N=169
  18. 24 — zeros(50!)=⌊50/5⌋+⌊50/25⌋=12 ⇒ (50!)² zeros=2×12
  19. 37 — differences: +3,+5,+7,+9 ⇒ next +11 ⇒ 26+11
  20. 0 — 99999 digit sum=45 divisible by 9 ⇒ remainder 0
  21. 36 — HCF(144,180)=36; HCF(36,252)=36
  22. 240 — LCM(16,20,24)=2⁴·3·5=240
  23. 84 — a·b=HCF·LCM ⇒ 105·x=21·420 ⇒ x=84
  24. 144 — HCF×LCM=product ⇒ 12×LCM=1728 ⇒ LCM=144
  25. 180 — LCM(12,15,18)=2²·3²·5=180 (minutes)
  26. 42 — HCF(84,126)=42
  27. 24 — largest square tile = HCF(96,120)=24
  28. 257 — N≡5 (mod7,9,12) ⇒ N−5 divisible by LCM(7,9,12)=252 ⇒ N=257
  29. 2 — 2³≡1 (mod7), 103 mod3=1 ⇒ 2¹⁰³≡2
  30. 8 — φ(13)=12, 123 mod12=3 ⇒ 5¹²³≡5³=125≡8 (mod13)
  31. 1 — 7 mod9 cycle: 7,4,1 (length3), 222 mod3=0 ⇒ remainder 1
  32. 1 — 11≡−1 (mod12), (−1)⁵⁰=1
  33. 6 — mod7: 2⁵⁰: 50 mod3=2 ⇒ 2²=4; 3⁵⁰: 50 mod6=2 ⇒ 3²=2 ⇒ sum=6
  34. 9 — 13 last digit 3; 3 cycle (3,9,7,1), 202 mod4=2 ⇒ 9
  35. 5 — 2⁹⁹⁹ last digit 8; 3⁹⁹⁹ last digit 7 ⇒ 8+7=15 ⇒ 5
  36. 01 — 3²⁰≡1 (mod100), 100 multiple of 20 ⇒ 3¹⁰⁰≡1 ⇒ last two digits 01
  37. 7 — 7 cycle (7,9,3,1), 2025 mod4=1 ⇒ 7
  38. 249 — zeros in 1000! = 200+40+8+1
  39. 31 — zeros in 125! = 25+5+1
  40. 97 — v₂(100!)=50+25+12+6+3+1=97
  41. 124 — v₅(500!)=100+20+4=124
  42. 22 — v₁₂(50!) = min(⌊v₂/2⌋, v₃); v₂=47 ⇒⌊/2⌋=23, v₃=22 ⇒ 22
  43. 60 — 5P3=5×4×3=60
  44. 96 — 5-digit using 0..4 (all digits): total 5!=120; leading 0 invalid: 4!=24 ⇒ 96
  45. 75220 — descending arrangement
  46. 20257 — smallest: first 2 then 0 then 2,5,7
  47. 2664 — sum digits=12, (n−1)!=2, 111 ⇒ 12×2×111=2664
  48. 36 — squares: 1²,2²,3²,4²,5² ⇒ next 6²
  49. 42 — differences: +3,+5,+7,+9 ⇒ next +11 ⇒ 31+11
  50. 96 — ×2 each step ⇒ 48×2
  51. 21 — triangular numbers: +2,+3,+4,+5 ⇒ next +6
  52. 162 — ×3 each step ⇒ 54×3
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