Mastery

Number Play — Mastery

30 questions 30 min Full-chapter mastery

Q1. According to the parity rules summarised the result of (odd) ± (even) is always
- A. Even
- B. Odd
- C. Zero
- D. Could be either, depending on the numbers
Q2. In the positive–negative token model a positive token paired with a negative token cancels to give zero. A teacher uses this model to show that 5 − 3 has the same parity as 5 + 3. The BEST classroom takeaway from this activity is
- A. The token model works only for sums, not for differences
- B. Negative tokens always make the answer odd
- C. Only odd numbers can be represented with tokens
- D. Pairing cancels tokens in pairs of two, so removing or adding any number of paired tokens preserves the leftover's parity
Q3. Two even numbers, both leaving remainder 2 when divided by 4, are added. Using algebra (4p + 2) + (4q + 2), the sum equals
- A. 4(p + q), which need not be a multiple of 4
- B. 4(p + q) + 2, which leaves remainder 2
- C. 8(p + q), which is a multiple of 8
- D. 4(p + q + 1), which is a multiple of 4
Q4. Statement P: Every number of the form 5k + 3 (k ≥ 0) leaves remainder 3 when divided by 5. Statement Q: Every number of the form 5k − 2 (k ≥ 1) also leaves remainder 3 when divided by 5. Which is correct?
- A. Only P
- B. Only Q
- C. Both P and Q describe the same set of numbers
- D. Neither P nor Q
Q5. Generalises: if a number A is divisible by k, then every multiple of A is also divisible by k. Which example below confirms this rule?
- A. 12 is divisible by 4; 12 × 7 = 84 is divisible by 4
- B. 12 is divisible by 4; 4 is divisible by 12
- C. 10 is divisible by 5; 30 is divisible by 7
- D. 15 is divisible by 6; 30 is divisible by 6
Q6. Three natural numbers each leave remainder 2 when divided by 6. Their sum, when divided by 6, leaves remainder
- A. 0
- B. 2
- C. 4
- D. Cannot be determined
Q7. Consider the statement: 'The sum of an odd number and an even number is always a multiple of 6.' This statement is
- A. Always true
- B. Sometimes true
- C. Never true
- D. True only when both numbers are below 10
Q8. Examines place values for the divisibility-by-11 rule: 10 = 11 − 1, 100 = 99 + 1, 1000 = 1001 − 1, 10000 = 9999 + 1, and so on. This shows that place values are alternately
- A. All one more than a multiple of 11
- B. All one less than a multiple of 11
- C. Alternately one less and one more than a multiple of 11
- D. Always exact multiples of 11
Q9. To test whether 5184 is divisible by 6 without dividing, a student uses the LCM-and-coprime idea. Which pair of checks is BOTH sufficient AND uses coprime factors of 6?
- A. Check divisibility by 2 and by 3
- B. Check divisibility by 1 and by 6
- C. Check divisibility by 2 and by 4
- D. Check divisibility by 3 and by 9
Q10. Rohan claims: 'Any number divisible by both 4 and 6 must be divisible by 24.' Which single number BEST disproves Rohan's claim?
- A. 12 — it is divisible by 4 and 6 but not by 24
- B. 8 — it is divisible by 4 but not by 6
- C. 18 — it is divisible by 6 but not by 4
- D. 24 — it is divisible by all three
Q11. An 8-digit number has digital root 7. Adding 10 to this number changes its digital root to
- A. 7
- B. 8
- C. 9
- D. 1
Q12. The digital root of any multiple of 3 must be one of
- A. {1, 2, 3}
- B. {3, 6, 9}
- C. {0, 3, 9}
- D. Any single digit from 1 to 9
Q13. A teacher finds that her Class 8 students can recite the digit-sum rule for 9 but cannot explain WHY it works. According to the NCF-2023 spirit reflected in Number Play, the BEST next step is
- A. Drill more numbers until students can apply the rule faster
- B. Show that 10 = 9 + 1, 100 = 99 + 1, 1000 = 999 + 1 — so each place value contributes its digit as remainder on division by 9
- C. Move on to the divisibility rule for 11 immediately
- D. Tell students the rule is a 'trick' that does not need explanation
Q14. A student tests whether 124 is divisible by 4 by adding the digits: 1 + 2 + 4 = 7, and concludes that since 7 is not divisible by 4, 124 is not divisible by 4. This conclusion is WRONG because
- A. The digit-sum test works only for 9 and 3, not for 4
- B. The student added the digits in the wrong order
- C. 124 has only three digits — too few for digit-sum tests
- D. The digit sum should be multiplied by 4, not divided
Q15. In the cryptarithm AB + 37 = 6A (each letter a distinct digit, leading digits nonzero, A and B different from 3 and 7), the value of A is
- A. 2
- B. 5
- C. 6
- D. 9
Q16. Anshu writes 7 as the sum of two consecutive natural numbers. Which equation captures her observation?
- A. 7 = 1 + 6
- B. 7 = 2 + 5
- C. 7 = 3 + 4
- D. 7 = 0 + 7
Q17. A teacher asks Class 8 students to predict the parity of 124 − 38 + 56 without computing. Using only the rule (even) ± (even) = (even) from, the result must be
- A. Odd
- B. Even
- C. A multiple of 4
- D. Cannot be decided without computing
Q18. Simplifies (4p + 2) + (4q + 2) step by step. Which line correctly expresses the simplified form as a single multiple of 4?
- A. 4p + 4q + 4 = 4(p + q) + 4
- B. 4p + 4q + 4 = 4(p + q + 1)
- C. 4p + 4q + 4 = 4(p + q) + 2
- D. 4p + 4q + 4 = 8(p + q)
Q19. The chapter draws an analogy between two ideas. Idea X: (even) + (odd) gives an odd number. Idea Y: (multiple of 4) + (4q + 2) gives an even number that is NOT a multiple of 4. The analogy works because
- A. In both, mixing the two 'types' yields the 'other' type — odd in X, non-multiple-of-4 in Y
- B. In both, mixing the two types yields the 'same' type as the first one
- C. Idea Y is a special case of Idea X applied to odd numbers
- D. There is no real analogy; the two ideas are unrelated
Q20. A general rule: if a number A is divisible by both k and m, then A is also divisible by
- A. k + m
- B. k × m
- C. The LCM of k and m
- D. The HCF of k and m
Q21. Consider the statement: 'If a number A is divisible by 7, then A is divisible by every multiple of 7.' Using examples, this statement is
- A. Always true
- B. Sometimes true
- C. Never true
- D. True only when A is a prime number
Q22. The digital root of a natural number is defined as the result of
- A. Multiplying its digits together once
- B. Adding the digits of the number repeatedly until a single digit is obtained
- C. Subtracting the smallest digit from the largest digit
- D. Counting the number of digits in the number
Q23. A number N is 1 more than some multiple of 6 (i.e., N = 6k + 1). Which of the following CANNOT be the digital root of N?
- A. 1
- B. 4
- C. 7
- D. 5
Q24. A student adds 487 + 296 and writes the answer 783. She checks her work using digital roots. Which check confirms the answer is consistent (without proving it correct)?
- A. Digital root of 487 is 1; of 296 is 8; of 783 is 9; 1 + 8 = 9 — consistent
- B. Digital root of 487 is 1; of 296 is 8; of 783 is 6; 1 + 8 = 9 ≠ 6 — definitely correct
- C. Digital root of 487 is 4; of 296 is 2; of 783 is 7; 4 + 2 = 6 ≠ 7 — consistent
- D. Digital root of any sum is always 9 — answer must be correct
Q25. A Class 8 student claims: 'If the digital root of a number is even, then the number itself must be even.' Which single counterexample disproves the claim?
- A. 11 — its digital root is 2 (even), but 11 itself is odd
- B. 18 — its digital root is 9 (odd), but 18 itself is even
- C. 20 — its digital root is 2 (even), and 20 itself is even
- D. 13 — its digital root is 4 (even), and 13 is odd
Q26. A Class 8 teacher plans to teach 'why the digit-sum test for 9 works'. Which is the BEST first step, in the spirit of Number Play ?
- A. Make students memorise: 'A number is divisible by 9 if digit sum is divisible by 9'
- B. Ask students to write 10, 100, 1000 as (multiple of 9) + 1 and notice the pattern
- C. Drill 50 numbers and ask students to apply the rule quickly
- D. Show a digital-root calculator and let students verify on a screen
Q27. Two teachers compare approaches to 'sum of two evens is a multiple of 4'. Teacher A draws block diagrams of 4p and 4q + 2 and asks students which combinations stack into groups of 4. Teacher B states the rule and gives 20 sums to verify. Which is BETTER aligned with the chapter's pedagogy?
- A. Teacher A — visualisation reveals WHY the rule holds and when it fails
- B. Teacher B — verification builds speed which is what CTET tests
- C. Both are equally aligned; the choice is style
- D. Teacher B if students are Hindi-medium, Teacher A otherwise
Q28. Which sequence of teaching steps BEST uses the positive–negative token manipulative to convince Class 8 students that a + b − c − d and a + b + c + d share the same parity?
- A. Drill parity rules → show tokens → state conclusion
- B. Place tokens for a, b, c, d → flip the sign of c and of d (each flip removes 2 tokens of one colour and adds 2 of the other) → observe parity unchanged → generalise
- C. Compute both expressions for specific numbers → see they are equal → conclude same parity
- D. Tell students the result and ask them to memorise it for the exam
Q29. In a 'conjecture-share-listen' classroom routine on the always/sometimes/never task , a student claims: 'The sum of two odd numbers is a multiple of 4.' What is the teacher's BEST next move?
- A. Tell the student the claim is wrong and move on
- B. Ask the student for one example, then a second example, and listen — let counterexamples like 1 + 3 = 4 vs 1 + 5 = 6 emerge from the student's own checking
- C. Set up a written test to see who else makes this mistake
- D. Ignore the claim because it is partly true
Q30. A Class 8 student writes: 'Since 4 × 6 = 24, any number divisible by 4 and 6 must be divisible by 24.' The teacher wants to diagnose the root error. The student's main mistake is
- A. Confusing 'divisible by both' with 'divisible by sum' instead of product
- B. Multiplying instead of adding 4 and 6
- C. Using k × m in place of LCM(k, m) when k and m are not coprime (here 4 and 6 share factor 2)
- D. Not checking the example with a calculator first

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