**Selina Concise Class 8 Math Chapter 5 Playing with Numbers Exercise 5D Solutions**

**EXERCISE 5D**

**For what value of digit x, is:**

(1) 1 + x + 5 is divisible by 3

⇒ 6 + x is a multiple of 3

⇒ 6 + x = 0, 3, 6, 9, 12, 15, 18, 21, 24, ……

⇒ x = – 6, – 3, 0, 3, 6, 9, 12, 15, ……

Since, x is digit ∴ x = 0, 3, 6 or 9.

(2) 31 + x + 5 is divisible by 3

⇒ 36 + x is a multiple of 3

⇒ 36 + x = 0, 3, 6, 9, 12, 15, 18, 21, 24, ……

⇒ x = – 36, – 33, – 30, …….., -3, 0, 3, 6, 9, 12, 15, ……

Since, x is digit ∴ x = 0, 3, 6 or 9.

(3) 28 + x + 6 is divisible by 3

⇒ 34 + x is a multiple of 3

⇒ 34 + x = 0, 3, 6, 9, 12, 15, 18, 21, 24, ……

⇒ x = – 34, – 31, ……. – 3, 0, 3, 6, 9, 12, 15, ……

Since, x is digit ∴ x = 0, 3, 6 or 9.

(4) 24x is divisible by 6, if it is divisible by 2 and 3 both.

24x is divisible by 2

⇒ 2 + 4 + x is divisible by 2

⇒ 6 + x = 0, 2, 4, 6, 8, 10, …….

⇒ x = – 6, – 4, – 2, 0, 2, 4, 6, ….. ………….(i)

24x is divisible by 3

⇒ 6 + x = 0, 3, 6, 9, 12, 15, …….

⇒ x = – 6, – 3, 0, 3, 6, 9, ……. ………..(ii)

Value of digit x common to equations (i) and (ii) is 0 and 6.

(5) 3×26 is divisible by 6, if it is divisible by 2 and 3 both.

3×26 is divisible by 2

⇒ 3 + x + 2 + 6 is divisible by 2

⇒ 11 + x = 0, 2, 4, 6, 8, 10, …….

⇒ x = – 11, – 9, – 7, -5, …., 1, 3, 5, ….. ………….(i)

24x is divisible by 3

⇒ 11 + x = 0, 3, 6, 9, 12, 15, …….

⇒ x = – 11, – 8, ….., 1, 4, 7, 9, ……. ………..(ii)

Value of digit x common to equations (i) and (ii) is 1 and 4 or 7.

(6) 42×8 is divisible by 4

⇒ 4 + 2 + x + 8 is multiple of 4

⇒ 14 + x = 0, 4, 8, 12, ….

⇒ x = – 14, – 10, ……, – 2, 2, 4, 6, 8

Since, x is a digit 2, 4, 6, 8.

(7) 9142x is multiple of 4

⇒ 9 + 1 + 4 + 2 + x is multiple of 4

⇒ 16 + x = 0, 4, 8, 12, …….

⇒ x = – 16, – 12, ……, 0, 4, 8, …..

∴ x = 0, 4 or 8.

(8) 7 + x + 3 + 4 is multiple of 9

⇒ 14 + x = 0, 9, 18, 27, 36, ….

⇒ x = – 5, 4, 13, ….

∴ x = 4

(9) 5 + x + 5 + 5 + 5 is multiple of 9

⇒ 20 + x = 0, 9, 18, 27, ….

⇒ x = – 20, – 11, – 2, 7, 16

∴ x = 7

(10) Sum of digit in even place = x

And sum of digit in odd place = 3 + 2 = 5

Difference between two sum = x – 5

3×2 is a multiple of 11

⇒ x – 5 = 0, 11, 22, 33…..

⇒ x = 5, 16, 27, ….

∴ x = 5

(11) Sum of digit in even place = x

And sum of digit in odd place = 5 + 2 = 7

Difference between two sum = x – 7

5×2 is a multiple of 11

⇒ x – 7 = 0, 11, 22, 33…..

⇒ x = 7, 18, 29, ….

∴ x = 7