Playing with Numbers (Class 8)

What this worksheet covers

This is an eighteen-question practice worksheet on playing with numbers for Class 8, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on playing with numbers at Class 8 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5In every puzzle, different letters stand for different digits and no number begins with 0.

Sample questions from this worksheet

A preview of what's inside Playing with Numbers (Class 8) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. A two-digit number with tens digit a and units digit b can be written in general form as _______.

   • Aa + b
   • Bab
   • C10b + a
   • D10a + bcorrect
   Solution: The tens digit stands for a lots of ten and the units digit for b ones, so the number is 10a + b. For example, 47 = 10(4) + 7.

2. 2. If the number 31z5 is divisible by 9, the smallest possible value of z is _______.

   • A0correct
   • B3
   • C6
   • D9
   Solution: Digit sum = 3 + 1 + z + 5 = 9 + z. For this to be a multiple of 9, z must be 0 or 9.
   The smaller of these is 0, giving 3105 = 9 × 345. ✓

3. 3. Consider the following statements.(i) If a number is divisible by 8, it is divisible by 4.(ii) If a number is divisible by 3 and by 5, it is divisible by 15.(iii) Every number divisible by 2 is divisible by 6.Which of the statements is/are correct?

   • A(i) and (ii) onlycorrect
   • B(ii) and (iii) only
   • C(i) and (iii) only
   • DAll three
   Solution: Statement (i) is true — 8 is itself a multiple of 4, so every multiple of 8 is a multiple of 4. Statement (ii) is true; 3 and 5 have no common factor, so a common multiple must be a multiple of 3 × 5 = 15. Statement (iii) is false; 4 is divisible by 2 but not by 6. Hence (i) and (ii).