"Question 3 If 24x is a multiple of 3, where x is a digit, what is the value of x? (Since 24x is a multiple of 3, its sum of digits 6 + x is a multiple of 3; so 6 + x is one of these numbers: 0, 3, 6, 9, 12, 15, 18…. But since x is a digit, it can only be that 6 + x = 6 or 9 or 12 or 15. Therefore, x = 0 or 3 or 6 or 9. Thus, x can have any of four different values)
Class 8 Playing with Numbers Page 260"
Answers
Numbers can be written in general form. Hence, a two digit number ab will be written as ab = 10a + b.
The general form of numbers is helpful in solving puzzles or number games.
Rules to be followed while solving the puzzles:.
Each letter in the puzzle must stand for just one digit. Each digit must be represented by just one letter. The first digit of a number cannot be zero.
The reasons for the divisibility of numbers by 10, 5, 2, 9 or 3 can be given when numbers are written in general form
Tests of Divisibility
Divisibility by 10
A number is divisible by 10 when its one’s digit is 0.
Divisibility by 5
If the ones digit of a number is 0 or 5, then it is divisible by 5.
Divisibility by 2
If the one’s digit of a number is 0, 2, 4, 6 or 8 then the number is divisible by 2
Divisibility by 9 and 3
A number is divisible by 9 if the sum of its digits is divisible by 9.
A number is divisible by 3 if the sum of its digits is divisible by 3.
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Solution:
Since 24x is a multiple of 3.
According to the divisibility rule of 3, the sum of all the digits should be a multiple of 3.
Here, the sum of digits of 24x is = 2 + 4+ x
∴ 2 + 4+ x=6 + x
Since ‘x’ is a digit.
6 +x= 6
x = 0
6 + x = 9
x = 3
6 + x= 12
x = 6
6 + x = 15
x= 9
Since x is a single digit number, the sum of the digits can be 6 or 9 or 12 or 15 and thus, the value of x comes to 0 or 3 or 6 or 9
Therefore, x can have any of the four different values.
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Hope this will help you....
Answer:
Step-by-step explanation: