Playing with Numbers (Class 6)

What this worksheet covers

This is an eighteen-question practice worksheet on playing with numbers for Class 6, 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 6 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. 5Rough work may be done in the space at the side of each page.

Sample questions from this worksheet

A preview of what's inside Playing with Numbers (Class 6) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. The prime factorisation of 180 is _______.

   • A2² × 3 × 5²
   • B2³ × 3 × 5
   • C2 × 3³ × 5
   • D2² × 3² × 5correct
   Solution: Divide by primes: 180 ÷ 2 = 90, 90 ÷ 2 = 45, 45 ÷ 3 = 15, 15 ÷ 3 = 5, and 5 is prime.
   So 180 = 2 × 2 × 3 × 3 × 5 = 2² × 3² × 5.

2. 2. Three lights flash at intervals of 20, 30 and 45 seconds. If they flash together now, after how many seconds will they next flash together?

   • A180 scorrect
   • B120 s
   • C90 s
   • D360 s
   Solution: They flash together again after the LCM of the intervals.
   20 = 2² × 5, 30 = 2 × 3 × 5, 45 = 3² × 5.
   LCM = 2² × 3² × 5 = 180 seconds (3 minutes).

3. 3. Consider the following statements.(i) The HCF of two numbers is always a factor of their LCM.(ii) If a number is divisible by 9, it is divisible by 3.(iii) The product of any two consecutive whole numbers is always odd.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 — every common factor divides every common multiple. Statement (ii) is true, because 9 is itself a multiple of 3. Statement (iii) is false; of any two consecutive numbers one is even, so the product is always even — for example 3 × 4 = 12. Hence (i) and (ii).