Number System MCQs with Answers – Solved from Past Papers
53 solved Number System MCQs collected from real PPSC, FPSC, SPSC, KPPSC, BPSC & NTS past papers (2002–2025). Tap an option to attempt — see correct answer instantly. Download the full PDF for offline revision.
Find LCM of 27 & 63?
Show solution
27 = 3³ and 63 = 3² × 7. LCM takes the highest power of each prime: 3³ × 7 = 27 × 7 = 189.
The sum of three consecutive integers is 33. Find the smallest integer?
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Let smallest = x. Then x + (x+1) + (x+2) = 33, so 3x + 3 = 33 → x = 10.
If 1is added to the largest four-digit number, the number becomes?
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Largest 4-digit number is 9999. Adding 1 gives 10000 (smallest 5-digit number).
What is the HCF of 18 and 30?
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18 = 2 × 3² and 30 = 2 × 3 × 5. Common factors: 2 × 3 = 6. So HCF = 6.
The sum of three consecutive even natural number is 78. Find the greater of these numbers?
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Let evens be x, x+2, x+4. Sum = 3x + 6 = 78 → x = 24. Greatest = 24 + 4 = 28.
The sum of two numbers is 138, and their difference is 68. What is the smallest number?
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If a + b = 138 and a − b = 68, then smaller b = (138 − 68) ÷ 2 = 70 ÷ 2 = 35.
What is the first prime number?
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1 is not prime (only one divisor). The first prime number is 2 (divisors: 1 and 2).
What is the sum of the first 5 composite numbers?
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First 5 composite numbers are 4, 6, 8, 9, 10. Sum = 4 + 6 + 8 + 9 + 10 = 37.
The sum of the first five prime numbers is?
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First 5 primes: 2, 3, 5, 7, 11. Sum = 2 + 3 + 5 + 7 + 11 = 28.
What is the LCM of 6" and 7" term in an=3n+2?
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With aₙ = 3n + 2: a₆ = 20 and a₇ = 23. HCF(20,23) = 1, so LCM = 20 × 23 = 460.
How many numbers of two digits are divisible by 9?
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Two-digit multiples of 9: 18, 27, 36, 45, 54, 63, 72, 81, 90, 99 — that is 10 numbers.
The sum of three consecutive odd numbers is 105. Who is the smallest number?
Show solution
Let smallest odd = x. Then x + (x+2) + (x+4) = 105 → 3x + 6 = 105 → x = 33.
What is the greatest possible length of a scale that can be used to measure exactly the lengths 3m, 5m 10cm, and 12m 90cm²
Show solution
Convert to cm: 300, 510, 1290. HCF(300,510) = 30; HCF(30,1290) = 30. Greatest scale = 30 cm.
Greatest Common Divisor of two numbers is 8 while their Least Common Multiple is 144. Find the other number if one number is 16?
Show solution
Product of two numbers = HCF × LCM. So 16 × b = 8 × 144 = 1152 → b = 1152 ÷ 16 = 72.
LCM stands for?
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LCM = Least Common Multiple. Among the given options, 'Least common' matches the abbreviation.
The sum of three consecutive integers is 48. What is the smallest integer?
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x + (x+1) + (x+2) = 48 → 3x + 3 = 48 → x = 15. Smallest integer is 15.
The sum of first five prime numbers is?
Show solution
First five primes: 2, 3, 5, 7, 11. Sum = 28.
How many prime numbers are less than 50?
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Primes < 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 — that is 15 primes.
How many two digit numbers are there which are divisible by 6?
Show solution
Two-digit multiples of 6: from 12 to 96. Count = (96 − 12) ÷ 6 + 1 = 15.
The greatest number which exactly divides 1050 and 750 is?
Show solution
1050 = 2 × 3 × 5² × 7 and 750 = 2 × 3 × 5³. HCF = 2 × 3 × 5² = 150.
Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is divisible by 4 or 6?
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Out of 36 outcomes: sums divisible by 4 (4,8,12) → 3+5+1 = 9 cases; sums divisible by 6 (6,12) → 5+1 = 6 cases; overlap (12) = 1. Union = 9 + 6 − 1 = 14. Probability = 14/36 = 7/18.
The sum of first 45 natural numbers is?
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Sum of first n naturals = n(n+1)/2 = 45 × 46 / 2 = 1035.
Three numbers which are co-prime to one another are such that the product of the first two is 551 and that of the two last numbers is 1073. The sum of the three numbers is?
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551 = 19 × 29 and 1073 = 29 × 37. The three coprime numbers are 19, 29, 37. Sum = 85.
The sum of the digits of a two-digit number is 13. If 9 is added to the number, the digits are reversed. What is the number?
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Let digits a,b with a+b = 13. Adding 9 reverses: (10a+b) + 9 = 10b + a → b − a = 1. Solving: a=6, b=7. Number = 67.
The sum of the digits of a two-digit number is 11. On adding 27 to the given number, its digits are reversed. Find the number?
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Digits a+b = 11. (10a+b) + 27 = 10b+a → b − a = 3. Solving: a=4, b=7. Number = 47.
The product of two numbers is 750 and the LCM product of is 150. What is their HCF?
Show solution
Product of two numbers = HCF × LCM. So HCF = 750 ÷ 150 = 5.
423 a divisible by?
Show solution
423 = 9 × 47, so 423 is divisible by 47 (only 47 among the options divides 423 exactly).
Find the largest number which divides 62, 132 and 237 to leave the same remainder in each case?
Show solution
For same remainder, take differences: 132−62 = 70, 237−132 = 105, 237−62 = 175. HCF(70,105,175) = 35.
The HCF of two numbers is 11 and their LCM is 693. If one of the numbers is 77, find the other?
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Product = HCF × LCM = 11 × 693 = 7623. Other number = 7623 ÷ 77 = 99.
Find the number of numbers from 1 to 100 which are not divisible by 2?
Show solution
Numbers 1 to 100 not divisible by 2 are odd numbers: 1, 3, 5, …, 99 — that is 50 numbers.
The sum of four consecutive even integers is 1284. The greatest of them is?
Show solution
Let evens be x, x+2, x+4, x+6. Sum = 4x + 12 = 1284 → x = 318. Greatest = 318 + 6 = 324.
The LCM of two numbers 60 and 100 is?
Show solution
60 = 2² × 3 × 5 and 100 = 2² × 5². LCM = 2² × 3 × 5² = 300.
What is the smallest integer divisible by both 25 and 30?
Show solution
Smallest integer divisible by both = LCM(25,30). 25 = 5², 30 = 2·3·5 → LCM = 2 × 3 × 5² = 150.
The sum of four consecutive integers is 1290. The greatest of them is?
Show solution
Let integers x, x+1, x+2, x+3. Sum = 4x + 6 = 1290 → x = 321. Greatest = 321 + 3 = 324.
HCF of 60 and 72 is?
Show solution
60 = 2² × 3 × 5 and 72 = 2³ × 3². HCF = 2² × 3 = 12.
Sum of Prime Numbers between 60 and 80?
Show solution
Primes between 60 and 80: 61, 67, 71, 73, 79. Sum = 61 + 67 + 71 + 73 + 79 = 351.
148 is divisible by?
Show solution
148 ÷ 37 = 4 exactly, so 148 is divisible by 37.
The number 329 is divisible by?
Show solution
329 ÷ 7 = 47 exactly (7 × 47 = 329), so 329 is divisible by 7.
When nis divided by 4, the remainder is 3. What is the remainder when 2n is divided by 4?
Show solution
If n mod 4 = 3, then 2n mod 4 = (2 × 3) mod 4 = 6 mod 4 = 2.
Find the greatest 3/2, 2/5, 5/7?
Show solution
Decimals: 3/2 = 1.5, 2/5 = 0.4, 5/7 ≈ 0.714. Largest is 3/2.
The largest four-digit number exactly divisible by 88 is?
Show solution
9999 ÷ 88 = 113.6… Take floor 113 × 88 = 9944. Largest 4-digit multiple of 88 is 9944.
If 1/3 of the liquid contents of a can evaporates on the first day and 3/4 of the remainder evaporates on the second day, the fractional part of the original contents remaining at the close of the second day is?
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After day 1, remaining = 1 − 1/3 = 2/3. Day 2 evaporates 3/4 of 2/3, leaving 1/4 × 2/3 = 2/12 = 1/6.
What is the smallest integer divisible by 21 and 18 and 24?
Show solution
21 = 3·7, 18 = 2·3², 24 = 2³·3. LCM = 2³ × 3² × 7 = 8 × 9 × 7 = 504.
What is the sum of all prime numbers from 60 to 80?
Show solution
Primes from 60 to 80: 61, 67, 71, 73, 79. Sum = 351.
How many numbers between 100 and 300 are divisible by 11?
Show solution
Multiples of 11 between 100 and 300: smallest 110, largest 297. Count = (297 − 110)/11 + 1 = 187/11 + 1 = 17 + 1 = 18.
Acertain number when divided by 899 gives a remainder 63 What is the remainder when the same number is divided by 29?
Show solution
899 = 29 × 31, so 899 is a multiple of 29. Number = 899k + 63, hence remainder when divided by 29 = 63 mod 29 = 63 − 58 = 5.
How many numbers up to 100 are divisible by 7?
Show solution
Multiples of 7 up to 100: 7, 14, …, 98. Count = floor(100/7) = 14.
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is?
Show solution
Let odds be x, x+2, x+4. Condition: 3x = 2(x+4) + 3 → 3x = 2x + 11 → x = 11. Third integer = 11 + 4 = 15.
The total number of digits used in numbering the pages of a book having 366 pages is?
Show solution
Pages 1–9 use 9 digits; pages 10–99 use 90 × 2 = 180 digits; pages 100–366 use 267 × 3 = 801 digits. Total = 9 + 180 + 801 = 990.
How many numbers between 100 and 300 are divisible by both 7 and 11?
Show solution
Divisible by both 7 and 11 means divisible by 77. Between 100 and 300: 154 and 231 — that is 2 numbers.
Smallest natural number is?
Show solution
Natural numbers start from 1, so the smallest natural number is 1.
Smallest prime number is?
Show solution
1 is not prime. The smallest prime is 2 (the only even prime).
Sum of three consecutive even numbers is 60. The greatest number is?
Show solution
Let evens be x, x+2, x+4. Sum = 3x + 6 = 60 → x = 18. Greatest = 18 + 4 = 22.
Number System MCQs for PPSC, FPSC, NTS & All Pakistani Competitive Exams
Number System is one of the most fundamental topics in Pakistani competitive exam Math. From PPSC Lecturer, Sub-Inspector and Tehsildar tests to FPSC CSS Screening (MPT), NTS NAT/GAT, OTS, CTS, KPPSC, SPSC, BPSC and AJKPSC — almost every paper contains 1 to 5 number-system questions. Mastering this one topic alone can secure 2–5 marks in any One Paper format exam because the same LCM, HCF, divisibility and digit patterns repeat verbatim across years.
QuizWing has compiled 53 verified number system MCQs from real past papers spanning 2002–2025 — every question solved from scratch by AI and answer keys verified. The bank covers LCM & HCF, prime numbers, divisibility rules, factors & multiples, remainder problems, digit-finding problems, and consecutive-integer puzzles.
What types of number system questions appear?
- LCM & HCF — “Find LCM of 27 & 63” → 189 (via prime factorization)
- Divisibility problems — “If 347xy is divisible by 80, find x + y”
- Consecutive integers — “Sum of three consecutive integers is 33; find the smallest” → 10
- Largest / smallest n-digit number — “1 added to the largest 4-digit number gives?” → 10000
- Remainder problems — modular arithmetic; “Number ÷ 899 gives remainder 63; find remainder ÷ 29”
- Number of factors — for N = p1^a × p2^b × p3^c → factors = (a+1)(b+1)(c+1)
- Sum of natural numbers — n(n+1)/2 for first n natural numbers
Key number system formulas
Divisibility rules to memorise
- ÷ 2 — last digit is even (0, 2, 4, 6, 8)
- ÷ 3 — sum of digits divisible by 3
- ÷ 4 — last two digits divisible by 4
- ÷ 5 — last digit is 0 or 5
- ÷ 6 — divisible by both 2 and 3
- ÷ 8 — last three digits divisible by 8
- ÷ 9 — sum of digits divisible by 9
- ÷ 10 — last digit is 0
- ÷ 11 — alternating digit sum divisible by 11 (e.g. for 4675: 4 − 6 + 7 − 5 = 0 ✓)
Mental-math shortcuts
- First 25 primes — memorise: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
- Euclidean algorithm for HCF — repeatedly replace (a, b) with (b, a mod b) until one is 0
- LCM shortcut — find HCF first, then LCM = (a × b) ÷ HCF
- Consecutive integer sum — if total = T and n integers, smallest = (T − n(n−1)/2) ÷ n
- Sum of digits — useful for both ÷ 3 and ÷ 9 checks
- Largest n-digit = (10^n) − 1; smallest n-digit = 10^(n−1)
How to use this page for revision
Quiz mode: Tap any option — green = correct, red = wrong. Use the pagination buttons to move between sets of 25 MCQs at a time.
PDF download: Click Download PDF in the sticky bar to grab all 53 MCQs with answers for offline study.
Mixed practice: attempt our full PPSC Mock Test with all subjects + weighted distribution to simulate the real exam.
Number System weightage by exam
| Exam | Typical Number System MCQs | Marks Share |
|---|---|---|
| PPSC One Paper | 1–3 | 2–5 |
| FPSC Screening | 2–5 | 4–8 |
| NTS NAT / GAT | 3–6 | 5–10 |
| CSS Screening (MPT) | 3–6 | 6–12 |
| OTS / CTS | 2–4 | 3–7 |
| SPSC / KPPSC / BPSC | 1–3 | 2–5 |
All MCQs sourced from official past papers of PPSC, FPSC, SPSC, KPPSC and NTS. Found a wrong answer? WhatsApp 0302-1417839 — we fix every reported issue within 24 hours.
Frequently Asked Questions
Typically 1 to 3 number system MCQs appear in every PPSC One Paper test (Sub-Inspector, Tehsildar, Junior Clerk, Lecturer, BPS-14/16/17). FPSC, NTS and CSS papers tend to include 2–5. Mastering this topic alone secures 2–5 guaranteed marks because LCM, HCF, divisibility and digit problems repeat verbatim.
Based on our analysis of 53 past-paper MCQs (2002–2025), the three most-recurring types are: (1) LCM and HCF using prime factorization, (2) divisibility-rule based digit problems (find missing digit), and (3) remainder problems using modular arithmetic.
No. Calculators are not allowed in PPSC, FPSC, NTS, OTS or any provincial commission exam. Practise mental math shortcuts — 10%, 25%, 50% calculations should take under 5 seconds.
Yes for PPSC and FPSC — 0.25 marks deducted per wrong answer. Strategy: if you can eliminate 2 out of 4 options confidently, attempt it; otherwise leave blank.
Yes — click the Download PDF button in the sticky bar at the top of the quiz section. You get all 53 MCQs with answers in a branded QuizWing PDF, free, no signup.
Yes — 100% transferable. All provincial public service commissions follow a near-identical Math syllabus. The same number system MCQs appear (often verbatim) in SPSC, KPPSC, BPSC, AJKPSC and NTS NAT/GAT papers.
Message us on WhatsApp at 0302-1417839 with the question number and what you believe the correct answer should be. We verify against multiple sources and fix every reported issue within 24 hours.