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
