Number Play — Mastery

Q1. On a number line marked from 1000 to 10000 in steps of 1000, where would the number 2754 be placed?

• A. Exactly at 3000
• B. Just after 2000, closer to 2000 than to 3000
• C. Between 7000 and 8000
• D. Just before 3000, closer to 3000 than to 2000

Q2. On a number line, 2010 and 2020 are marked with one tick-mark gap between them. Each tick represents 5 units. What number lies two ticks to the left of 2010?

• A. 1990
• B. 2000
• C. 2005
• D. 2015

Q3. On a number line, 86,705 and 87,705 are marked. The remaining 8 tick positions extend to the right. What is the largest number in the visible 10-tick sequence?

• A. 87,705
• B. 96,705
• C. 1,86,705
• D. 92,705

Q4. Find the digit sum of 49. Then find the digit sum of 58. What pattern do you notice for numbers 40 to 70?

• A. Digit sums are all odd
• B. Digit sums are all multiples of 7
• C. Digit sums equal the tens digit
• D. Digit sum of 49 = 13, of 58 = 13 — moving along, the digit sum stays the same when one digit drops by 1 and the other rises by 1

Q5. The footnote mentions one famous 3-digit starting number for which the reverse-and-add process is suspected never to give a palindrome. Which number?

• A. 89
• B. 169
• C. 196
• D. 289

Q6. What is the difference between the largest and smallest 5-digit palindromes?

• A. 89,998
• B. 89,899
• C. 90,000
• D. 89,998 cannot be the answer

Q7. The student is asked to repeat Kaprekar's process with 3-digit numbers. Which number eventually repeats (the 3-digit Kaprekar constant)?

• A. 297
• B. 495
• C. 576
• D. 999

Q8. Jeevan asks: 'Will any year's calendar repeat exactly in a future year?' What is the smallest gap (in years) after which a non-leap year's calendar typically repeats?

• A. Every year — calendars are the same yearly
• B. 100 years exactly
• C. 6 or 11 years, depending on intervening leap years
• D. Never — every year is unique

Q9. Manish's birthday 20/12/2012 (dd/mm/yyyy) is special because

• A. The digits 2, 0, 1, 2 repeat in that order
• B. It is a leap year
• C. It is the same date as Republic Day
• D. It is the largest date in 2012

Q10. After 11:11, what is the next palindromic time on a 12-hour clock, and how many minutes later does it occur?

• A. 12:21, after 70 minutes
• B. 12:12, after 61 minutes
• C. 12:21, after 71 minutes
• D. 12:00, after 49 minutes

Q11. Using the middle-column numbers 25,000, 400, 13,000, 1,500 and 60,000 (added any number of times), why is it impossible to make exactly 1,000?

• A. Because 1,000 is a 4-digit number
• B. Because 1,500 > 1,000, so we cannot use 1,500 at all
• C. Because 60,000 is much larger than 1,000
• D. Because all middle numbers are 400 or larger, and none combine to give 1,000

Q12. Always, Sometimes or Never: a 5-digit number minus a 2-digit number gives a 3-digit number.

• A. Always true
• B. Sometimes true
• C. True only if the 5-digit number ends in 0
• D. Never true

Q13. A Class 6 teacher writes four statements on the board: I. A 5-digit + 5-digit number is a 5-digit number. II. A 4-digit + 2-digit number is a 4-digit number. III. A 4-digit + 2-digit number is a 6-digit number. IV. A 5-digit − 2-digit number is a 5-digit number. Which TWO are 'Sometimes' true?

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

Q14. On, the (a) pattern has 8 boxes of 40 in the top rows, 9 boxes of 50 in the middle and lower-middle rows, and 4 boxes of 40 at the bottom. Total 12 forties (480) and 9 fifties (450). What is the sum?

• A. 830
• B. 880
• C. 920
• D. 930

Q15. Choose a number between 210 and 390 and create a number pattern that sums to it. If a child picks 250 and uses only 50s, how many 50-cells are needed?

• A. 3
• B. 4
• C. 5
• D. 6

Q16. Lothar Collatz conjectured in 1937 that for any starting whole number, the Collatz process will

• A. Always reach 1
• B. Always reach a power of 2
• C. Always cycle without ending
• D. Never repeat any number

Q17. Why is the Collatz conjecture obviously true for the powers of 2 (1, 2, 4, 8, 16, 32, …)?

• A. Because powers of 2 are always odd
• B. Because halving a power of 2 always gives a smaller power of 2, eventually reaching 1
• C. Because powers of 2 are never divisible by 3
• D. Because of Kaprekar's constant

Q18. In which year did Lothar Collatz first state the conjecture that every whole number under his process reaches 1?

• A. 1900
• B. 1937
• C. 1949
• D. 1975

Q19. The student is asked to estimate the distance between Gandhinagar (Gujarat, west India) and Kohima (Nagaland, north-east India). Which is the most reasonable estimate?

• A. About 250 km
• B. About 850 km
• C. About 2,800 km
• D. About 12,000 km

Q20. 'Name some objects around you that are a few thousand in number, and more than ten thousand in number.' Which pair fits this prompt for a typical school setting?

• A. Pages in your textbook (a few thousand); blades of grass on the school field (more than ten thousand)
• B. Pencils in the school (more than ten thousand); books in the library (a few thousand)
• C. Children in your class (a few thousand); students in your school (more than ten thousand)
• D. Birds on a tree (a few thousand); stars in the sky (a few thousand)

Q21. Roshan wants to make fruit custard for 5 people using milk and 3 types of fruit. He estimates the cost at ₹100. As a Class 6 teacher, what is the BEST way to judge Roshan's estimate?

• A. Accept it without question — estimates need not be checked.
• B. Reject it immediately — costs are always more than ₹100.
• C. Reason that 1 L milk and small portions of 3 fruits for 5 people are likely to cost ₹300–₹500 in India in 2026, so ₹100 is an under-estimate.
• D. Compute the exact cost using a kitchen scale before commenting.

Q22. In Game #2, what number does the winning player aim to reach first, and what range can each player add per turn?

• A. Reach 99; add 1 to 10
• B. Reach 21; add 1 to 3
• C. Reach 50; add 1 to 5
• D. Reach 100; add 2 to 5

Q23. Starting from 0, players alternate adding 1, 2 or 3. First to reach 22 wins. What is the winning strategy for the first player?

• A. Always say 1 first, then reach 6, 10, 14, 18, 22.
• B. Always say 2 first, then reach 6, 10, 14, 18, 22.
• C. Always say 3 first, then reach 7, 11, 15, 19, 22 (this is wrong because last gap is 3).
• D. There is no winning strategy for the first player; the second player always wins.

Q24. A Class 6 teacher in Rampur wants to use the '21-game' (Game #1) to develop mental-math habits in the class. Which is the BEST pedagogic move at the start?

• A. Show the winning sequence 1, 5, 9, 13, 17, 21 directly so students don't waste time.
• B. Let pairs play freely 3–4 times, then ask 'who keeps winning and why?' to draw out the pattern.
• C. Ban any discussion until each child plays alone 20 times.
• D. Skip the game and give students a worksheet of similar arithmetic instead.

Q25. Fill a 9-cell table so that the cell with the SECOND-LARGEST number is NOT a supercell. One valid arrangement is

• A. 9, 8, 7, 6, 5, 4, 3, 2, 1 in order
• B. 5, 6, 7, 8, 9, 4, 3, 2, 1 (placing 8 next to 9)
• C. 1, 9, 2, 8, 3, 7, 4, 6, 5 (alternating)
• D. 1, 2, 3, 4, 5, 6, 7, 9, 8 (placing 9 next to 8)

Q26. 'Mental Math' demonstrates which two operations on numbers as quick shortcuts?

• A. Multiplication and division
• B. Squaring and cubing
• C. Estimation and rounding
• D. Addition and subtraction

Q27. A student in Class 6 finishes the (c) pattern by listing 'value × count' for each shaded region instead of adding cell by cell. Which is the BEST description of what she has done?

• A. Repeated addition to find the total
• B. Applied multiplication as a shortcut for repeated addition — exactly the computational-thinking idea the chapter promotes
• C. Used estimation instead of an exact answer
• D. Reordered the addition using the commutative law only

Q28. The chapter summary lists 'thinking about and formulating set procedures to use numbers' as a useful skill. What term does the summary use for this skill?

• A. Symbolic thinking
• B. Algorithmic intuition
• C. Computational thinking
• D. Numerical estimation

Q29. 'How big a number can you form having the digit sum of 14? Can you make an even bigger number?' What does the solution reveal about the answer?

• A. The biggest is 5,000,000,000,000
• B. The biggest is 99,999
• C. There is no biggest — you can always pad zeros to make an arbitrarily large number with digit sum 14
• D. The biggest is 50,000,000

Q30. The chapter summary lists FOUR different purposes for which numbers can be used. Which of these is NOT one of them?

• A. Convey information
• B. Estimate magnitudes
• C. Memorise multiplication tables faster
• D. Play and win games