Which of the following numbers is prime?

For 127, test only the primes 2, 3, 5, 7 and 11, since √127 is less than 12. None divides it, so 127 is prime.

The five-digit number 4a7b2 is divisible by 36. What is the greatest possible value of a + b?

Divisibility by 4 requires b to be odd. The digit sum is 13 + a + b, so a + b must be 5 or 14 for divisibility by 9; 14 is possible with a = 9 and b = 5.

What is the least perfect square divisible by both 24 and 40?

LCM of 24 and 40 is 120 = 2³ × 3 × 5. Make each exponent even: 2^4 × 3² × 5² = 3600.

Find the sum of the cubes of the first 9 natural numbers.

The sum of cubes is the square of the sum: (9 × 10 ÷ 2)² = 45² = 2025.

How many positive factors of 2^5 × 3^4 × 5² are odd multiples of 9?

An odd factor has exponent 0 for 2. The exponent of 3 can be 2, 3 or 4, and that of 5 can be 0, 1 or 2, giving 3 × 3 = 9 factors.

What is the unit digit of 6^125 + 8^42?

Every positive power of 6 ends in 6. Since 42 leaves remainder 2 on division by 4, 8^42 ends in 4; 6 + 4 = 10 gives unit digit 0.

What is the smallest five-digit number exactly divisible by 27?

10000 = 27 × 370 + 10. Add 27 − 10 = 17 to obtain 10017.

A number leaves remainder 17 when divided by 28. What remainder does it leave when divided by 7?

Write the number as 28q + 17. Since 28q is divisible by 7, the remainder is that of 17 ÷ 7, namely 3.

Find the remainder when 3^100 is divided by 17.

3^4 = 81 leaves remainder 13, and 3^8 leaves remainder −1 modulo 17, so 3^16 leaves remainder 1. Since 100 = 16 × 6 + 4, the required remainder is 13.

Evaluate 998 × 1002.

Use (1000 − 2)(1000 + 2) = 1000² − 2² = 1000000 − 4 = 999996.

What is the greatest digit x for which 6x34 is divisible by 6?

The last digit is even, so only divisibility by 3 remains. The digit sum 13 + x is a multiple of 3 for x = 2, 5 or 8; the greatest is 8.

How many integers n satisfy 20 < √n < 21?

Squaring gives 400 < n < 441. The integers from 401 to 440 total 440 − 401 + 1 = 40.

A positive integer has exactly 24 positive factors. Its prime factorisation is 2^a × 3², where a is a non-negative integer. Find a.

The factor count is (a + 1)(2 + 1) = 24. Hence a + 1 = 8 and a = 7.

In an arithmetic progression, the first term is 8 and the common difference is 6. Which term is 152?

Solve 8 + (n − 1) × 6 = 152. Thus n − 1 = 24 and n = 25.

What are the last two digits of 3^40?

3^10 ends in 49, so 3^20 ends in 49² = 2401, hence in 01. Squaring again shows that 3^40 also ends in 01.

The sum of the first n positive even integers is 870. Find n.

The sum is n(n + 1), so n(n + 1) = 870 = 29 × 30. Therefore n = 29.

How many consecutive positive integers n satisfy that n! has exactly 24 trailing zeros?

100! has 20 + 4 = 24 trailing zeros, and the count stays 24 through 104!. At 105! it becomes 21 + 4 = 25, so there are 5 values.

What is the least positive integer that leaves remainder 2 when divided by 5 and remainder 3 when divided by 7?

Numbers leaving remainder 2 on division by 5 begin 2, 7, 12, 17. The first of these leaving remainder 3 on division by 7 is 17.

If x + 1/x = 5 and x ≠ 0, find x³ + 1/x³.

Use x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x). The value is 5³ − 3 × 5 = 110.

A number is divided by 9, giving quotient q and remainder 7. If the same number is divided by 7, the quotient is q + 4 and the remainder is 1. Find the number.

Equate the two forms: 9q + 7 = 7(q + 4) + 1. Thus 2q = 22, q = 11 and the number is 9 × 11 + 7 = 106.

Using each of the digits 0, 4, 7 and 8 exactly once, what is the greatest four-digit number divisible by 4?

The first two digits can be 87, leaving 4 and 0. Both 40 and 04 are divisible by 4, and 8740 is the greater arrangement.

A three-digit number has hundreds digit 3 more than its units digit. Its tens digit is twice its units digit, and its digit sum is 19. Find the number.

784. Let the units digit be u. Then (u + 3) + 2u + u = 19, giving u = 4; the digits are 7, 8 and 4.

Find the remainder when 12^35 − 1 is divided by 11.

12 leaves remainder 1 on division by 11. Therefore 12^35 − 1 leaves remainder 1^35 − 1 = 0.

What is the least positive integer that must be added to 6,700 to obtain a perfect cube?

18³ = 5832 and 19³ = 6859. The next perfect cube is 6859, so add 6859 − 6700 = 159.

How many ordered digit pairs (a, b) make the four-digit number 5a2b divisible by 15?

For divisibility by 5, b = 0 or 5. If b = 0, a can be 2, 5 or 8; if b = 5, a can be 0, 3, 6 or 9, giving 3 + 4 = 7 pairs.

Topic

Number System MCQ – Part 3 - Topic Guide and MCQs

Q: How long is the Number System MCQ – Part 3 quiz?

Number System MCQ – Part 3 runs 25 untimed questions - about 25 min at a steady pace. The set clears at 40% and you can retake it as often as you like.

Q: What kind of questions does Number System MCQ – Part 3 ask?

The set answers that: each question carries four options and a full explanation, so you learn the wording an examiner uses, not just the fact behind it.

Q: Where else can I practise Quantitative Aptitude?

Open the quiz page above, or start from the Quantitative Aptitude subject page if you want to drill neighbouring lanes in the same sitting.

Q: Do my scores save?

Scores, bookmarks and streaks need the optional Google sign-in. Opening the set and answering questions does not.

Part of Quantitative Aptitude > 01 Number System - 25 questions, about 25 min, with an explanation after every answer.

Question count

about 25 min

Estimated time

Mixed

Difficulty

03 Nov 2026

Last updated

Quick answer

Number System MCQ – Part 3 is a topic inside Quantitative Aptitude (01 Number System). It runs 25 untimed MCQs - roughly 25 min - and the review explains every answer once you submit.

Topic introduction

What Number System MCQ – Part 3 covers

The shape of the set before you start it.

Number System MCQ – Part 3 sits inside Quantitative Aptitude, under the 01 Number System lane, and the portal keeps it as one self-contained set: 25 questions, four options each, no clock and a written explanation behind every answer.

Attempt it once to find the gaps, read why each distractor is wrong, then retake the same set a few days later. The questions you miss twice are the ones worth writing down.

Curated by Gurpreet Singh · Punjab Police SI, Rank 2 (713/800) · Founder, House of Aspirants · Read his story →

Question bank

Number System MCQ – Part 3: all 25 questions

Read the question, pick an option, then open the answer.

Which of the following numbers is prime?
1. 119
2. 121
3. 127
4. 133
Show answer

Answer: (C) 127

Explanation: For 127, test only the primes 2, 3, 5, 7 and 11, since √127 is less than 12. None divides it, so 127 is prime.
The five-digit number 4a7b2 is divisible by 36. What is the greatest possible value of a + b?
1. 14
2. 5
3. 17
4. 18
Show answer

Answer: (A) 14

Explanation: Divisibility by 4 requires b to be odd. The digit sum is 13 + a + b, so a + b must be 5 or 14 for divisibility by 9; 14 is possible with a = 9 and b = 5.
What is the least perfect square divisible by both 24 and 40?
1. 120
2. 900
3. 14400
4. 3600
Show answer

Answer: (D) 3600

Explanation: LCM of 24 and 40 is 120 = 2³ × 3 × 5. Make each exponent even: 2^4 × 3² × 5² = 3600.
Find the sum of the cubes of the first 9 natural numbers.
1. 729
2. 2025
3. 4050
4. 285
Show answer

Answer: (B) 2025

Explanation: The sum of cubes is the square of the sum: (9 × 10 ÷ 2)² = 45² = 2025.
How many positive factors of 2^5 × 3^4 × 5² are odd multiples of 9?
1. 15
2. 18
3. 9
4. 45
Show answer

Answer: (C) 9

Explanation: An odd factor has exponent 0 for 2. The exponent of 3 can be 2, 3 or 4, and that of 5 can be 0, 1 or 2, giving 3 × 3 = 9 factors.
What is the unit digit of 6^125 + 8^42?
1. 0
2. 2
3. 4
4. 8
Show answer

Answer: (A) 0

Explanation: Every positive power of 6 ends in 6. Since 42 leaves remainder 2 on division by 4, 8^42 ends in 4; 6 + 4 = 10 gives unit digit 0.
What is the smallest five-digit number exactly divisible by 27?
1. 10008
2. 10026
3. 9990
4. 10017
Show answer

Answer: (D) 10017

Explanation: 10000 = 27 × 370 + 10. Add 27 − 10 = 17 to obtain 10017.
A number leaves remainder 17 when divided by 28. What remainder does it leave when divided by 7?
1. 1
2. 3
3. 4
4. 5
Show answer

Answer: (B) 3

Explanation: Write the number as 28q + 17. Since 28q is divisible by 7, the remainder is that of 17 ÷ 7, namely 3.
Find the remainder when 3^100 is divided by 17.
1. 4
2. 9
3. 13
4. 16
Show answer

Answer: (C) 13

Explanation: 3^4 = 81 leaves remainder 13, and 3^8 leaves remainder −1 modulo 17, so 3^16 leaves remainder 1. Since 100 = 16 × 6 + 4, the required remainder is 13.
Evaluate 998 × 1002.
1. 1000004
2. 999004
3. 996004
4. 999996
Show answer

Answer: (D) 999996

Explanation: Use (1000 − 2)(1000 + 2) = 1000² − 2² = 1000000 − 4 = 999996.
What is the greatest digit x for which 6x34 is divisible by 6?
1. 9
2. 8
3. 7
4. 5
Show answer

Answer: (B) 8

Explanation: The last digit is even, so only divisibility by 3 remains. The digit sum 13 + x is a multiple of 3 for x = 2, 5 or 8; the greatest is 8.
How many integers n satisfy 20 < √n < 21?
1. 40
2. 39
3. 41
4. 42
Show answer

Answer: (A) 40

Explanation: Squaring gives 400 < n < 441. The integers from 401 to 440 total 440 − 401 + 1 = 40.
A positive integer has exactly 24 positive factors. Its prime factorisation is 2^a × 3², where a is a non-negative integer. Find a.
1. 6
2. 8
3. 7
4. 11
Show answer

Answer: (C) 7

Explanation: The factor count is (a + 1)(2 + 1) = 24. Hence a + 1 = 8 and a = 7.
In an arithmetic progression, the first term is 8 and the common difference is 6. Which term is 152?
1. 24
2. 26
3. 27
4. 25
Show answer

Answer: (D) 25

Explanation: Solve 8 + (n − 1) × 6 = 152. Thus n − 1 = 24 and n = 25.
What are the last two digits of 3^40?
1. 21
2. 01
3. 41
4. 81
Show answer

Answer: (B) 01

Explanation: 3^10 ends in 49, so 3^20 ends in 49² = 2401, hence in 01. Squaring again shows that 3^40 also ends in 01.
The sum of the first n positive even integers is 870. Find n.
1. 29
2. 28
3. 30
4. 31
Show answer

Answer: (A) 29

Explanation: The sum is n(n + 1), so n(n + 1) = 870 = 29 × 30. Therefore n = 29.
How many consecutive positive integers n satisfy that n! has exactly 24 trailing zeros?
1. 0
2. 4
3. 5
4. 10
Show answer

Answer: (C) 5

Explanation: 100! has 20 + 4 = 24 trailing zeros, and the count stays 24 through 104!. At 105! it becomes 21 + 4 = 25, so there are 5 values.
What is the least positive integer that leaves remainder 2 when divided by 5 and remainder 3 when divided by 7?
1. 12
2. 22
3. 32
4. 17
Show answer

Answer: (D) 17

Explanation: Numbers leaving remainder 2 on division by 5 begin 2, 7, 12, 17. The first of these leaving remainder 3 on division by 7 is 17.
If x + 1/x = 5 and x ≠ 0, find x³ + 1/x³.
1. 125
2. 110
3. 115
4. 140
Show answer

Answer: (B) 110

Explanation: Use x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x). The value is 5³ − 3 × 5 = 110.
A number is divided by 9, giving quotient q and remainder 7. If the same number is divided by 7, the quotient is q + 4 and the remainder is 1. Find the number.
1. 106
2. 97
3. 115
4. 99
Show answer

Answer: (A) 106

Explanation: Equate the two forms: 9q + 7 = 7(q + 4) + 1. Thus 2q = 22, q = 11 and the number is 9 × 11 + 7 = 106.
Using each of the digits 0, 4, 7 and 8 exactly once, what is the greatest four-digit number divisible by 4?
1. 8704
2. 8470
3. 8740
4. 7840
Show answer

Answer: (C) 8740

Explanation: The first two digits can be 87, leaving 4 and 0. Both 40 and 04 are divisible by 4, and 8740 is the greater arrangement.
A three-digit number has hundreds digit 3 more than its units digit. Its tens digit is twice its units digit, and its digit sum is 19. Find the number.
1. 748
2. 874
3. 682
4. 784
Show answer

Answer: (D) 784

Explanation: Let the units digit be u. Then (u + 3) + 2u + u = 19, giving u = 4; the digits are 7, 8 and 4.
Find the remainder when 12^35 − 1 is divided by 11.
1. 1
2. 0
3. 10
4. 2
Show answer

Answer: (B) 0

Explanation: 12 leaves remainder 1 on division by 11. Therefore 12^35 − 1 leaves remainder 1^35 − 1 = 0.
What is the least positive integer that must be added to 6,700 to obtain a perfect cube?
1. 441
2. 59
3. 159
4. 1300
Show answer

Answer: (C) 159

Explanation: 18³ = 5832 and 19³ = 6859. The next perfect cube is 6859, so add 6859 − 6700 = 159.
How many ordered digit pairs (a, b) make the four-digit number 5a2b divisible by 15?
1. 7
2. 6
3. 8
4. 4
Show answer

Answer: (A) 7

Explanation: For divisibility by 5, b = 0 or 5. If b = 0, a can be 2, 5 or 8; if b = 5, a can be 0, 3, 6 or 9, giving 3 + 4 = 7 pairs.

Why it matters

Why Number System MCQ – Part 3 is worth the hours

Where the marks actually come from.

Number System MCQ – Part 3 is factual rather than analytical: you either recall it in seconds or you lose the mark to somebody who did. That makes it one of the cheapest sections to convert - a handful of short sittings usually settles the whole cluster.

Exam relevance

Exams where Number System MCQ – Part 3 matters

Derived from the subject and lane this topic belongs to.

Punjab Police Constable

The highest-volume recruitment on this list. Build your base with Punjab GK and current affairs, then drill reasoning until speed is automatic.

Punjab Police ASI

Assistant Sub-Inspector papers separate candidates on English and Punjabi accuracy as much as on general awareness. Practise language daily.

Punjab Police Sub-Inspector (SI)

The most competitive paper here. Polity, history and quant reasoning decide the rank - so take full timed mocks before the exam.

Punjab Police Intelligence Assistant

Data handling, mental ability and computer awareness carry most of the weight. Use short topic sets and check every explanation.

Punjab Police Jail Warder

A tighter syllabus: general awareness, Punjabi and basic reasoning. Perfect for a daily quiz habit - short sessions, high consistency.

Patwari

Revenue work starts with Punjab geography, history and current affairs. Add quant for the sections that reward calculation speed.

Excise Inspector

General awareness and English carry this paper. Track Punjab policy news daily and revise it as MCQs, not as notes.

Naib Tehsildar

Land records, Punjab history and polity, plus data interpretation. A strong polity base is the fastest score to build.

Clerk

Grammar, comprehension, typing and basic computer knowledge. Accuracy beats speed here - review every wrong answer.

PSPCL jobs

Recruitment by the Punjab State Power Corporation Limited. Technical aptitude sits alongside general awareness and reasoning.

Punjab Police Head Constable

The communication and clerical tier of Punjab Police. Punjabi, English and general knowledge carry the paper, and computer awareness is worth real marks.

Staff Selection Commission

The central recruitment ladder most aspirants attempt alongside a state paper. Arithmetic, reasoning and English decide the score; general awareness decides the cutoff.

Railway Recruitment

A high-volume, high-speed paper. Arithmetic, reasoning and general awareness asked at a pace that punishes anyone still working out method during the attempt.

Banking Exams

Quantitative aptitude and reasoning at speed, with a separate English section and a general awareness paper that moves with the financial news cycle.

Expected questions

Expected questions from Number System MCQ – Part 3

What an examiner usually reaches for in this cluster.

Expect one-line recall questions - definitions, stand-for expansions, identifiers and the ordering of things. Practise the wording as well as the concept: these papers test terminology, and the set above uses the same four-option shape they do.

Daily habit

Keep the Expected MCQs habit running

20 fresh mixed questions a day, plus the current-affairs sets examiners keep reusing.

Daily Quiz Expected MCQs

Previous year questions

Previous Year Questions

How this topic behaves in real papers.

Past papers reuse clusters like this almost verbatim across years and posts. Run the same set until every distractor is familiar - previous-year style questions stop being recall and start being free marks.

Where the previous-year sets live

The portal's previous-year practice runs through the General Knowledge lane and the daily mixed quiz.

Previous Year Questions Daily Quiz

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Take the Number System MCQ – Part 3 quiz

25 questions, about 25 min, instant scoring and a full review at the end.

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Questions

Number System MCQ – Part 3 - common questions

Answered against the set as it is published today.

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