# 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 that6 + 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)

Since 24x is a multiple of 3, the sum of its digits is 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 …

Since x is a single digit number, the sum of the digits can be 6 or 9 or 12 or 15 and the value of x comes to 0 or 3 or 6 or 9 respectively

Thus, x can have its value as any of the four different values 0, 3, 6, or 9

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Quiz | Who will Win the Game?41 mins  Quiz on Divisibility Test32 mins  Divisible or not41 mins  Mastering Divisibility Test42 mins  NCERT | Divisibility Test43 mins  Smart Revision | Complete Chapter Quiz45 mins  Quiz | Imp. Qs. on Playing With Numbers45 mins  Properties of Rational Numbers29 mins  On the Number line44 mins  Essentials of Rational Numbers45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 