- No data uploaded
- Instant results
11+ Exam Number System & Simplification Questions
Practise number system & simplification (quantitative aptitude) for the UK 11+ (Eleven Plus) Grammar School Entrance: 10 multiple-choice questions, each with the correct answer and a worked explanation. Click an option to check it, or “New questions” for another set.
Number System & Simplification practice
-
Q1.Find the HCF of 63 and 18.
Show answer & explanation
Answer: D — 9
HCF(63, 18) = 9. Check: HCF × LCM = 9 × 126 = 1134 = product of the numbers.
-
Q2.Find the LCM of 20 and 20.
Show answer & explanation
Answer: C — 20
LCM(20, 20) = 20. Check: HCF × LCM = 20 × 20 = 400 = product of the numbers.
-
Q3.What is √5,625?
Show answer & explanation
Answer: C — 75
75 × 75 = 5625, so √5625 = 75.
-
Q4.Find the next number in the series: 1, 2, 4, 8, 16, ?
Show answer & explanation
Answer: C — 32
Each term is multiplied by 2.
-
Q5.Find the next number in the series: 3, 5, 9, 15, 23, ?
Show answer & explanation
Answer: A — 33
Differences are 2, 4, 6, 8 → next difference 10.
-
Q6.What is √1,764?
Show answer & explanation
Answer: C — 42
42 × 42 = 1764, so √1764 = 42.
-
Q7.Find the next number in the series: 49, 64, 81, 100, 121, ?
Show answer & explanation
Answer: B — 144
Squares of consecutive numbers: 7², 8², … → 12² = 144.
-
Q8.Find the LCM of 15 and 35.
Show answer & explanation
Answer: B — 105
LCM(15, 35) = 105. Check: HCF × LCM = 5 × 105 = 525 = product of the numbers.
-
Q9.Find the HCF of 4 and 14.
Show answer & explanation
Answer: B — 2
HCF(4, 14) = 2. Check: HCF × LCM = 2 × 28 = 56 = product of the numbers.
-
Q10.What is √1,024?
Show answer & explanation
Answer: B — 32
32 × 32 = 1024, so √1024 = 32.
How to approach number system & simplification questions
Learn squares to 30 and cubes to 15, apply BODMAS strictly, and use HCF × LCM = product of two numbers. For series, check the differences first, then the ratios.
About 11+ Exam
UK 11+ (Eleven Plus) Grammar School Entrance — conducted by Set by individual grammar schools and consortia. Selective school entrance taken in Year 6, typically covering maths, English, verbal and non-verbal reasoning.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
11+ Exam practice topics
| Topic | Section | Question source |
|---|---|---|
| Number System & Simplification | Quantitative aptitude | Calculated (new numbers every set) |
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Verbal Reasoning & Analogies | Reasoning | Calculated + question bank |
| Vocabulary & Idioms | English | Question bank |
| Logical Reasoning | Reasoning | Calculated (new numbers every set) |