Question

If 24 a is a multiple of 3 where a is a digit then the value of a is

Answer 1

Answer:

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 24a 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 24a is = 2 + 4+ a

∴  2 + 4+ a=6 + a

Since ‘a’ is a digit.

6 +a= 6

a = 0

 

6 + a = 9

a = 3

 

6 + a= 12

a= 6

 

6 + a = 15

a= 9

 

Since a 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

Answer 2

Answer:

3

Step-by-step explanation:

24a= 3

2+4+a=3

6+a=3

a=6-3

a=3