1. What is the remainder when 47 is divided by 5?
- A3
- B7
- C9
- D2
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Answer: D) 2
47 = 9 × 5 + 2, so the remainder is 2. (9 is the quotient.)
Class 8 Parity, Remainders and Digital Roots — practice questions with answers
Number System · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. What is the digital root of every multiple of 9 (other than 0)?
- A9
- BIt varies
- C0
- D1
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Answer: A) 9
Multiples of 9 have digit sums that are multiples of 9, and repeating the process ends at 9 (e.g. 7 × 9 = 63 → 9; 99 → 18 → 9).
3. 1 January of a non-leap year is a Thursday. What day of the week is 1 March of that year?
- AThursday
- BSaturday
- CSunday
- DMonday
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Answer: C) Sunday
From 1 Jan to 1 Mar is 31 + 28 = 59 days. 59 = 8 × 7 + 3, so it is 3 days after Thursday: Sunday.
4. Without working out 7⁴ in full, find its remainder on division by 5.
- A4
- B1
- C3
- D2
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Answer: B) 1
7 leaves 2 on division by 5. 2⁴ = 16, which leaves 1. Check: 7⁴ = 2401 = 5 × 480 + 1.
5. A number leaves a remainder of 23 when divided by 35. What remainder does it leave when divided by 7?
- A3
- B2
- C5
- D23
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Answer: B) 2
The number is 35k + 23. 35k is a multiple of 7, so only 23 matters: 23 = 3 × 7 + 2. The remainder is 2.
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