Number Play — Quiz

Q1. Ravi notes the parity rules. He picks two odd numbers, say 7 and 5. The result of 7 + 5 and the result of 7 − 5 are both

• A. Odd
• B. Even
• C. One odd and one even
• D. Cannot be decided without more information

Q2. Priya starts with the expression a + b − c − d and changes the +b to −b. According to the explanation by how much does the value of the expression change?

• A. By an odd number
• B. By the number a only
• C. By 2b, which is an even number
• D. By zero — the value stays the same

Q3. For any 4 numbers a, b, c, d, eight expressions of the form a ± b ± c ± d are possible. concludes that all eight expressions

• A. Always give the same final value
• B. Always give eight different odd values
• C. Always give exactly four even and four odd values
• D. Always share the same parity (all even or all odd)

Q4. On the textbook adds two multiples of 4, written as 4p and 4q. Using algebra, why must their sum always be a multiple of 4?

• A. Because adding two numbers always doubles the factor
• B. Because the sum of two even numbers is always a multiple of 4
• C. Because p + q is always even
• D. Because 4p + 4q = 4(p + q), so 4 is a factor of the sum

Q5. Examines adding a multiple of 4, written as 4p, to an even number that is not a multiple of 4, written as 4q + 2. What remainder does the sum leave when divided by 4?

• A. 0
• B. 1
• C. 2
• D. 3

Q6. Asks Anshu to write all natural numbers that leave a remainder 3 when divided by 5. Which algebraic expression captures all such numbers (for k ≥ 0)?

• A. 5k − 3
• B. 5k + 3
• C. 3k + 5
• D. 5 ÷ k + 3

Q7. Suppose 7 divides both 84 and 35. Using the general rule which of the following must 7 also divide?

• A. Only the product 84 × 35
• B. Only the quotient 84 ÷ 35
• C. 84 + 35 but not 84 − 35
• D. Both 84 + 35 and 84 − 35

Q8. Statement 2 says: 'If a number is divisible by 8, then 8 also divides any two numbers (separately) that add up to that number.' The textbook concludes this statement is

• A. True only for even numbers
• B. Always true
• C. Never true
• D. Sometimes true (depends on how the number is split)

Q9. Class 8 students discuss the statement 'The sum of two multiples of 3 is a multiple of 6.' Which classification fits best?

• A. Always true
• B. Never true
• C. Sometimes true
• D. True only for prime multiples

Q10. 10 = 9 + 1, 100 = 99 + 1, 1000 = 999 + 1, and so on. What does this pattern tell us when we divide any place value by 9?

• A. Each place value is itself a multiple of 9
• B. Each place value leaves remainder 1 when divided by 9
• C. Each place value leaves remainder 9 when divided by 10
• D. Place values cannot be divided by 9

Q11. Using the place-value method what is the remainder when 7309 is divided by 9?

• A. 4
• B. 9
• C. 7
• D. 1

Q12. The four-digit number 31z5 is divisible by 9, where z is a single digit. Using the digit-sum rule, the smallest possible value of z is

• A. 9
• B. 3
• C. 6
• D. 0

Q13. 'we can add the digits of a number repeatedly till a single digit is obtained. This single digit is the remainder when the number is divided by 9.' If the digital root of 7309 is 1, the remainder when 7309 is divided by 9 is

• A. 0
• B. 1
• C. 8
• D. 9

Q14. Traces digital roots back to a classical Indian work. The text says Aryabhata II's Mahasiddhanta (c. 950 CE) mentions the method of computing digital roots and that it was used to

• A. Predict the position of planets
• B. Measure the area of a circle
• C. Perform checks on arithmetic calculations
• D. Solve quadratic equations

Q15. While solving a cryptarithm AB + 37 = 6A Priya finds that B in the answer could be 0. Which cryptarithm rule from must she still respect for the letter A?

• A. A and B can stand for the same digit if the puzzle is symmetric
• B. Each letter may stand for several digits in turn
• C. A may equal zero only when it is in the units place
• D. The first digit of a number is never 0, so A cannot be 0