Question 3 - Fill in the steps - Playing with Numbers

Last updated at April 16, 2024 by Teachoo

Transcript

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.)We know that,
A Number is divisible by 3, if sum of digits is divisible by 3
24x
Sum of digits of 24x = 2 + 4 + x
= 6 + x
Let us check different values of x
& check if number is divisible by 3
Sum of digits = 6 + x
∴ x can be 0, 3, 6 or 9

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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