Q3. 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.)

Answers (1)

if a number is multiple of 3 then the sum of its digits is also a multiple of 3.

Summ of digits of 24x = 2 + 4 + x = 6 + x

6 + x is a multiple of 3 which means

6 + x = 0 or 3 or 9 or 12....

but since x is a single digit the possible sum is 6 or 9 or 12 or 15 and hence value of x are 0 or 3 or 6 or 9 respectively.

hence possible value of x = 0, 3, 6, or 9.

 

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