ICSE-VIII-Mathematics
05: Playing with Number Class 8 Maths
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- Qstn #53 × 26 a multiple of 6?Ans : × 26 is a multiple of 6
3 + x + 2 + 6 is a multiple of 3
⇒ 11 + x = 0, 3, 6, 9, 12, 15, 18, 21
⇒ x = -11, -8, -5, -2, 1, 4, 7, 10, ......
Since, x is a digit
x = 1, 4 or 7
- Qstn #642 × 8 divisible by 4?Ans : 42 × 8 is divisible by 4
⇒ 4 + 2 + x + 8 is a multiple of 2
⇒ 14 + x = 0, 2, 4, 6, 8,
⇒ x = -8, -6, -4, -2, 2, 4, 6, 8,
Since, x is a digit 2, 4, 6, 8
- Qstn #79142 × a multiple of 4?Ans : 9142 × a multiple of 4
⇒ 9 + 1 + 4 + 2 + x is a multiple of 4
⇒ 16 + x = 0, 4, 8, ........
x = -8, -4, 0, 4, 8
since, x is a digit 4, 8
- Qstn #87 × 34 divisible by 9?Ans : 7 × 34 is multiple of 9
⇒ 7 + x + 3 + 4 is a multiple of 9
⇒ 14 + x = 0, 9, 18, 27,
⇒ x = -1, 4, 13,
Since, x is a digit x = 4
- Qstn #95 × 555 a multiple of 9?Ans : Sum of the digits of 5 × 555
= 5 + x + 5 + 5 + 5 = 20 + x
It is multiple by 9
The sum should be divisible by 9
Value of x will be 7
- Qstn #103 × 2 divisible by 11?Ans : Sum of the digit in even place = x
And sum of the digits in odd place = 3 + 2 = 5
Difference of the sum of the digits in even places and in odd places = x - 5
3 × 2 is a multiple of 11
⇒ x - 5 = 0, 11, 22,
⇒ x = 5, 16, 27
Since, x is a digit x = 5
- Qstn #115 × 2 is a multiple of 11?Ans : Sum of digit in even place = x
And sum of the digits in odd place = 5 + 2 = 7
Difference of the sum of the digits in even places
And in odd places = x - 7
5 × 2 is a multiple of 11
⇒ x - 7 = 0, 11, 22
⇒ x - 7, 18, 29,
Since, x is a digit x = 7