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)

Solution:

We know that, according to divisibility rules, if the sum of the digits of a number is divisible by 3, then the given number is a multiple of 3.

• Since 24x is a multiple of 3, the sum of its digits is also a multiple of 3.
• Sum of digits of 24x = 2 + 4 + x = 6 + x. Hence, 6 + x is a multiple of 3.
• This is possible when 6 + x is any one of these numbers 0, 3, 6, 9, and so on ...

For, 6 + x = 0 ⇒ x = 0 - 6 = -6. Not possible as x is a single digit positive number.

For, 6 + x = 3 ⇒ x = 3 - 6 = -3. Not possible as x is a single digit positive number.

For, 6 + x = 6 ⇒ x = 6 - 6 = 0

For, 6 + x = 9 ⇒ x = 9 - 6 = 3

For, 6 + x = 12 ⇒ x = 12 - 6 = 6 

For, 6 + x = 15 ⇒ x = 15 - 6 = 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 out to be 0 or 3, 6 or 9 respectively.

Thus, x can have four different values 0, 3, 6, or 9.

☛ Check: NCERT Solutions for Class 8 Maths Chapter 16

Video Solution:

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 Maths NCERT Solutions - Chapter 16 Exercise 16.2 Question 3

Summary:

If 24x is a multiple of 3, where x is a digit, the value of x can take four different values that is 0, 3, 6 or 9.

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