Number Play — Mastery

Q1. Seven children stand in a line and call out 0, 1, 1, 2, 4, 1, 5 using the 'taller-in-front' rule. The last child in the line is

• A. The tallest of the seven children.
• B. Definitely the second-tallest.
• C. The shortest of the seven children.
• D. Standing right behind the tallest child.

Q2. Why must the tallest child in the line always call out the number '0', no matter where she stands?

• A. No child standing in front of her can be taller than her, so the count of taller children ahead is 0.
• B. She is the first in the line, so the count is 0 by default.
• C. She must stand at the back, so nobody is in front of her.
• D. Children at the back are forced by the rule to call out 0.

Q3. A teacher writes (even – even) on the board and asks for its parity. The correct answer, supported by an example, is

• A. Odd; for example 8 – 4 = 4.
• B. Sometimes odd, sometimes even; depends on the numbers.
• C. Odd; for example 10 – 6 = 4.
• D. Even; for example 8 – 4 = 4.

Q4. Consider the three statements: I. (odd – even) is always odd. II. (even – odd) is always odd. III. (odd – even) and (even – odd) have opposite parities. Which are correct?

• A. I and III only
• B. All three
• C. II and III only
• D. I and II only

Q5. Lakpa has an odd number of ₹1 coins, an odd number of ₹5 coins and an even number of ₹10 coins. He says the total in his piggy bank is ₹205. Did he make a mistake?

• A. Yes — the total must be even, so ₹205 is impossible.
• B. No — ₹205 is fine because ₹5 and ₹1 are both odd.
• C. Yes — the total must be a multiple of 10.
• D. No — odd plus odd plus even can be any number.

Q6. Without multiplying, the parity of 27 × 13 is

• A. Even, because the product has many digits.
• B. Cannot be decided without doing the multiplication.
• C. Odd, because odd × odd = odd.
• D. Even, because 27 + 13 = 40 is even.

Q7. Which single rule from the chapter explains the parity of 135 × 654 most efficiently?

• A. Odd × odd = odd, applied to both factors.
• B. The product of any two numbers is always even.
• C. Adding the digits of each number first decides parity.
• D. An even factor makes the whole product even.

Q8. About the expression 48w – 2 for whole numbers w, three statements: I. 48w is always even. II. 48w – 2 is always even. III. 48w – 2 can be made odd by choosing the right value of w. Which are correct?

• A. I and III only
• B. II and III only
• C. I only
• D. I and II only

Q9. When three of the numbers 1 to 9 (each used once) are placed in three circles of a grid, the smallest possible sum is 6 and the largest possible sum is

• A. 18
• B. 21
• C. 24
• D. 27

Q10. How many essentially different 3 × 3 magic squares can be made using the numbers 1 to 9, if we treat rotations and reflections of the same square as the same?

• A. Exactly one.
• B. Exactly three.
• C. Exactly eight.
• D. Infinitely many.

Q11. A 3 × 3 magic square is found carved on a pillar of an 8th century CE temple in

• A. Khajuraho, Madhya Pradesh.
• B. Konark, Odisha.
• C. Hampi, Karnataka.
• D. Palani, Tamil Nadu.

Q12. Virahanka described the sequence around 700 CE. Fibonacci wrote about the same numbers in Europe in 1202 CE. The gap between Virahanka and Fibonacci is roughly

• A. About 200 years.
• B. About 800 years.
• C. About 500 years.
• D. About 1500 years.

Q13. The chapter remarks that the number of petals on a daisy is usually a Virahanka number. Which of these daisy petal counts is NOT a Virahanka number from the sequence 1, 2, 3, 5, 8, 13, 21, 34, ...?

• A. 13
• B. 21
• C. 25
• D. 34

Q14. A light bulb is ON. Dorjee toggles its switch 77 times. The best parity-based reasoning to decide its final state is

• A. Each toggle flips the state, so after an odd number of toggles the bulb is OFF; 77 is odd, so the bulb is OFF.
• B. Each toggle changes the state; 77 is large so the bulb is ON.
• C. Each toggle flips the state, so after an even number of toggles the bulb is ON; 77 is odd, so the bulb is ON.
• D. Toggles cancel each other in pairs, so the bulb stays ON regardless of count.

Q15. A teacher asks students why the three row-sums of any 1-to-9 magic square must total 45. The best explanation is

• A. Because the three rows together contain each of 1 to 9 exactly once, so the row-sums add to 1 + 2 + … + 9 = 45.
• B. Because 45 is the magic sum of the square.
• C. Because every row has three numbers, and 3 × 15 = 45.
• D. Because 45 is the largest sum possible from any three of the numbers 1 to 9.

Q16. Under the 'taller-in-front' rule, a child who is neither first nor last in the line says '0'. This is

• A. Never true — only the first person can say 0.
• B. Only sometimes true — it happens when nobody ahead is taller than her.
• C. Always true — every middle person says 0.
• D. Never true — at least one taller child must stand ahead.

Q17. Two consecutive whole numbers in the parity chain are always

• A. Both even.
• B. Both odd.
• C. One even and one odd.
• D. Both prime.

Q18. Five numbers are added: two of them are even and three of them are odd. The sum is

• A. Even, because even numbers dominate the parity rule.
• B. Odd, because the three odd numbers leave one leftover.
• C. Sometimes odd, sometimes even — depends on the numbers chosen.
• D. Always zero.

Q19. Lakpa claims his piggy bank totals ₹205, with an odd number of ₹1 coins, an odd number of ₹5 coins and an even number of ₹10 coins. Which line of reasoning best shows his error?

• A. ₹205 is not a multiple of 5, so the ₹5 coins cannot make it.
• B. ₹10 × even gives even; ₹1 × odd + ₹5 × odd = odd + odd = even; total = even + even = even, not 205.
• C. Odd-many ₹1 coins must give ₹1 only, which contradicts ₹205.
• D. ₹205 cannot be reached with positive coins of value ₹1, ₹5, ₹10.

Q20. Without multiplying, the parity of the number of small squares in a 3 × 4 grid is

• A. Odd, because 3 is odd.
• B. Even, because at least one side (4) is even.
• C. Cannot be decided without multiplying 3 by 4.
• D. Odd, because 3 + 4 = 7 is odd.

Q21. The expression 2f + 3, where f is a whole number, gives

• A. Always even numbers.
• B. Always odd numbers.
• C. Both even and odd numbers, depending on f.
• D. Only multiples of 3.

Q22. In India, the 3 × 3 magic square made with numbers 1 to 9 is traditionally called the

• A. Chautisa Yantra.
• B. Navagraha Yantra.
• C. Kubera Yantra.
• D. Lo Shu Yantra.

Q23. Using the m-form magic square (centre m), if the centre number is 25, the magic sum is

• A. 25
• B. 50
• C. 75
• D. 125

Q24. The Chautisa Yantra at the Parshvanath Jain temple, Khajuraho is historically significant because it is the

• A. First-ever recorded 3 × 3 magic square.
• B. First-ever recorded 4 × 4 magic square.
• C. Largest known magic square in India.
• D. Only magic square with negative numbers.

Q25. According to the chapter, Virahanka's work on this number sequence was inspired by the earlier work of

• A. Pingala, around 300 BCE.
• B. Gopala, around 1135 CE.
• C. Hemachandra, around 1150 CE.
• D. Fibonacci, in 1202 CE.

Q26. Using short (1-beat) and long (2-beat) syllables, the number of different rhythms of total 6 beats is

• A. 8
• B. 10
• C. 13
• D. 21

Q27. In the cryptarithm UT + TA = TAT (each letter is a digit 0–9), the values are

• A. U = 1, T = 9, A = 0
• B. U = 9, T = 1, A = 0
• C. U = 0, T = 9, A = 1
• D. U = 9, T = 0, A = 1

Q28. Liswini finds 50 loose sheets fallen from her encyclopaedia, each printed on both sides. Can the sum of the page numbers on these sheets be 6000?

• A. No — 50 sheets give an odd sum, so 6000 (even) is impossible.
• B. Yes — each sheet has one even and one odd page; the sum of 50 such pairs is even, and 6000 is even.
• C. No — page numbers on loose sheets cannot add to a round figure like 6000.
• D. Yes — but only if exactly 25 sheets carry even pages on the front.

Q29. A news clip reads: '14,70,369 people got married last year.' A friend remarks, 'Shouldn't it be an even number?' The friend's reasoning is

• A. Correct — every marriage involves 2 people, so the total count must be even; 14,70,369 is odd.
• B. Correct — only even numbers can be written with commas in the Indian system.
• C. Wrong — the total can be any number; it need not be even.
• D. Wrong — large numbers are always reported approximately, so parity does not matter.

Q30. A Class 7 teacher wants students to see why (odd + odd) is even, without using algebra. The best classroom strategy is to

• A. Just state the rule 'odd + odd = even' and ask students to memorise it.
• B. Show that 3 + 5 = 8 and let students assume the rule from this one example.
• C. Draw each odd number as pairs of dots with one leftover, then pair the two leftovers together to form a new pair, showing the total can be arranged in pairs.
• D. Ask students to add many pairs of odd numbers on their calculators and observe.