Number Play – Class 8 Mathematics notes, important questions and MCQs

Chapter overview

Number puzzles use divisibility rules, place value and patterns. Knowing why a trick works is as important as using it.

Divisibility rules

• By 2: last digit even; by 5: ends in 0 or 5; by 10: ends in 0.
• By 3 / 9: sum of digits divisible by 3 / 9.
• By 4: last two digits divisible by 4; by 8: last three digits divisible by 8.
• By 11: difference between sums of alternate digits is 0 or a multiple of 11.

Number tricks with algebra

• A two-digit number ab = 10a + b; reversing gives 10b + a.
• (10a + b) + (10b + a) = 11(a + b), always divisible by 11.
• (10a + b) − (10b + a) = 9(a − b), always divisible by 9.

Key terms

Divisible

leaves no remainder on division

Digit sum

sum of all digits of a number

Divisibility rule

a quick test to check if one number divides another without actual division

Formulas

• ab = 10a + b
• ab + ba = 11(a + b)

Important questions with answers

Quick revision

• Divisible by 9 ⇔ digit sum divisible by 9.
• Reversing-and-subtracting gives a multiple of 9.
• Rule for 11 uses alternate digits.

Exam tips

• For "find the missing digit", use the digit-sum rule.
• A number divisible by both 2 and 3 is divisible by 6.

Practice MCQs

1. Which number is divisible by 3?

   1. 124
   2. 410
   3. 152
   4. 231
   Show answer

   Answer: (d) 231. 2 + 3 + 1 = 6.

2. A number ending in 0 is divisible by

   1. 10
   2. 7
   3. 3
   4. 9
   Show answer

   Answer: (a) 10. Rule for 10.

3. Is 6,72,104 divisible by 8?

   1. yes
   2. no
   3. only by 4
   4. cannot say
   Show answer

   Answer: (a) yes. Last three digits 104 = 8 × 13.

4. If 4x5 is divisible by 9, the digit x is

   1. 0
   2. 9
   3. 0 or 9
   4. 3
   Show answer

   Answer: (c) 0 or 9. 4 + x + 5 must be 9 or 18.

5. Which number is divisible by 9

   1. 4,325
   2. 5,551
   3. 6,103
   4. 7,281
   Show answer

   Answer: (d) 7,281. Digit sum 18.

6. The sum of a two-digit number and its reverse is always divisible by

   1. 9
   2. 10
   3. 7
   4. 11
   Show answer

   Answer: (d) 11. 11(a + b).

7. Which number is divisible by 11?

   1. 5731
   2. 9273
   3. 8162
   4. 1243
   Show answer

   Answer: (d) 1243. (1 + 4) − (2 + 3) = 0.

8. For 5A2 to be divisible by 3, the digit A can be

   1. 0
   2. 1
   3. 2
   4. 3
   Show answer

   Answer: (c) 2. 5 + A + 2 must be a multiple of 3; A = 2 gives 9.