Number Play — Practice

Q1. Anshu observes that every odd natural number can be written as the sum of how many consecutive natural numbers?

• A. Three consecutive numbers
• B. Four consecutive numbers
• C. Two consecutive numbers
• D. Five consecutive numbers

Q2. The sum of four consecutive natural numbers is 34. Which set are these numbers?

• A. 7, 8, 9 and 10
• B. 6, 7, 8 and 9
• C. 8, 9, 10 and 11
• D. 5, 6, 7 and 8

Q3. If p is the greatest of five consecutive natural numbers, the other four numbers in terms of p are

• A. p + 1, p + 2, p + 3, p + 4
• B. p − 2, p − 1, p + 1, p + 2
• C. p, p + 1, p + 2, p + 3
• D. p − 1, p − 2, p − 3, p − 4

Q4. Even numbers that are multiples of 4 leave which remainder when divided by 4?

• A. Remainder 1
• B. Remainder 0
• C. Remainder 2
• D. Remainder 3

Q5. An even number which is NOT a multiple of 4 leaves what remainder when divided by 4?

• A. 0
• B. 1
• C. 2
• D. 3

Q6. Priya writes the even number 30 in the form 4q + 2 (an even number that is not a multiple of 4). What is the value of q?

• A. 8
• B. 6
• C. 5
• D. 7

Q7. According to the general rule if a divides M and a divides N, then which of the following must be true?

• A. a divides both M + N and M − N
• B. a divides M × N but not M + N
• C. a divides M ÷ N
• D. a divides only M + N, never M − N

Q8. Generalises: if a number A is divisible by k, then A is divisible by which of the following?

• A. All multiples of k
• B. All factors of k
• C. Only k itself
• D. Only the prime factors of A

Q9. The shortcut: a number is divisible by 9 if and only if which of these is also divisible by 9?

• A. The number of digits
• B. The product of its digits
• C. The sum of its digits
• D. The first digit alone

Q10. Using the digit-sum method what is the remainder when 427 is divided by 9?

• A. 1
• B. 2
• C. 3
• D. 4

Q11. The shortcut for divisibility by 3 is similar to the one for 9. A number is divisible by 3 if

• A. The sum of its digits is divisible by 3
• B. Its last digit is 3
• C. Its first digit is divisible by 3
• D. The product of its digits is divisible by 3

Q12. The divisibility-by-11 shortcut: place alternating '+' and '−' signs before every digit starting from which digit?

• A. The first (leftmost) digit
• B. The middle digit
• C. The units (rightmost) digit
• D. Any digit you choose

Q13. An example: the digital root of the number 489710 is

• A. 1
• B. 2
• C. 9
• D. 11

Q14. The digital root of any multiple of 9 is always

• A. 0
• B. 1
• C. 3
• D. 9

Q15. A cryptarithm. Which statement about cryptarithm rules is correct?

• A. Each letter stands for one digit, each digit is represented by at most one letter, and the first digit of a number is never 0
• B. Each letter stands for any number of digits as long as the sum works out
• C. Two different letters may represent the same digit if the puzzle is hard
• D. The first digit of a number must always be 0 to begin the puzzle