Playing with Numbers · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Which of the following is a prime number?
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Answer: B) 11
11 has only two factors, 1 and 11, so it is prime. 9 = 3x3, 15 = 3x5, 21 = 3x7 are composite.
2. Two prime numbers whose difference is 1 are called consecutive primes if both are prime. Which pair of primes has a difference of exactly 1?
- A2 and 3
- B3 and 5
- C5 and 7
- D11 and 13
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Answer: A) 2 and 3
2 and 3 are both prime and differ by 1. They are the only such pair, since any two consecutive numbers other than this include an even composite.
3. A number is prime. Which statement must be true about it?
- AIt is always odd
- BIt has exactly two factors
- CIt is always even
- DIt has exactly three factors
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Answer: B) It has exactly two factors
By definition a prime has exactly two factors, 1 and itself. It need not be odd (2 is prime).
4. How many composite numbers are there between 1 and 20?
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Answer: B) 11
Composite numbers from 1 to 20 are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20 — that is 11 numbers.
5. A magician in Delhi says: 'Take any prime number greater than 3. When you divide it by 6, the remainder is always 1 or 5.' Test this rule with the primes 7, 11, 13 and 17.
How many of these four primes leave a remainder of 1 when divided by 6?
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Answer: C) 2
67 leaves remainder 1, 611 leaves 5, 613 leaves 1, 617 leaves 5. So remainder 1 occurs for 7 and 13 — that is 2 primes.