Extra Questions for Class 7 Maths Chapter 6: Number Play – HOTS

Fresh HOTS practice questions for Class 7 Maths Chapter 6 “Number Play”, testing parity, magic squares, and the Virahanka sequence with new numbers. These Class 7 Mathematics Chapter 6 important questions are handy for last-minute exam practice.

Q1.

Is the sum of 7 odd numbers always odd or even? Verify with an example.

Answer: Always odd (an odd count of odd numbers always sums to odd). Example: 1+3+5+7+9+11+13 = 49 (odd).

Q2.

A 3×3 magic square has centre value 12. What is its magic sum, and what would the magic sum become if every number were tripled?

Answer: Magic sum = 3×12 = 36. After tripling every number, the new magic sum = 36×3 = 108.

Q3. Assertion-Reason

Assertion (A): The product of two odd numbers is always odd.
Reason (R): An odd number can be written as 2k+1 for some integer k, and the product of two such numbers is also of the form 2m+1.

Answer: Both A and R are true, and R correctly explains A.

Q4.

What are the next two terms after 4181 in the sequence 1, 2, 3, 5, 8, 13, …, 2584, 4181?

Answer: 2584+4181 = 6765; 4181+6765 = 10946

Q5. Spot the error

A student claims: “Since 6j−4 gives 2, 8, 14, 20 for j=1,2,3,4, it must generate all even numbers.” Explain the error.

Answer: This is incorrect. The expression 6j−4 only produces numbers that increase in steps of 6 (2, 8, 14, 20, …), so it skips many even numbers like 4, 6, 10, 12, etc. It generates only some even numbers, not all of them.

Q6.

In how many ways can 5 be written as an ordered sum of 1s and 2s?

Answer: This equals the Virahanka term for n=5, which is 8 ways (matching the sequence 1,2,3,5,8,…).

Q7.

A bulb starts OFF. It is toggled 124 times. Is it ON or OFF at the end?

Answer: Since 124 is even, an even number of toggles returns the bulb to its starting state, so it will be OFF.

Q8.

Solve the cryptarithm: AA + B = CDD, where each letter is a single digit and AA means a 2-digit number with both digits equal to A.

Answer: Try A=9: AA=99. 99+B=CDD (a 3-digit number starting with C). For B=1: 99+1=100, so C=1, D=0, D=0. This gives A=9, B=1, C=1, D=0 (99+1=100 checks out).

Q9.

Is 10×15 odd or even? Explain using the parity rule for products.

Answer: Even. Since at least one of the two numbers (10) is even, the product must be even, regardless of the other factor. (10×15 = 150, which is even.)

Q10.

Create a magic square using the numbers 4 to 12 (9 consecutive numbers). What is its magic sum?

Answer: Add 3 to every cell of the classic 1–9 magic square (since 4 = 1+3). New magic sum = 15 + 3(3) = 24.

NCERT Solutions: Class 7 Maths Chapter 6

Revision Notes: Class 7 Maths Chapter 6 Revision Notes

Written by Satish

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