Math, asked by BrainlyHelper, 1 year ago

"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

Answered by nikitasingh79
102

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....

Answered by manjotp2
26

Answer:


Step-by-step explanation:


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