 Hi and welcome to the session. If 2 for x is a multiple of 3 where x is a digit, what is the value of x? Now before moving on to the solution let us understand that number n is divisible by 3 if the sum of its digits is also divisible by 3. We will use this fact as our key idea to solve the given question. Let us now move on to the solution. Now we are given in the question that 2 for x is a multiple of 3 or we can say 2 for x is divisible by 3. Now using the fact given in key idea we can say this number is divisible by 3 so sum of its digits that is 2, 4 and x is also divisible by 3. Or we can say sum of 2, 4 and x is a multiple of 3 so we can write since 2 for x is a multiple of 3 so sum of its digits that is 2 plus 4 plus x is divisible by 3. Now 2 plus 4 is 6 so we can write that is 6 plus x is a multiple of 3. Now this is possible when 6 plus x is equal to 0, 3, 6, 9, 12, 15, 18, 21, 24 and other higher multiples of 3. Now we know that x represents the digit so its value must lie between 0 and 9. Now if we take 6 plus x equal to 0 then we get the value of x as minus 6. Subtracting 6 from both the sides of this equation we get x is equal to minus 6. Now minus 6 does not lies between 0 and 9 so this is not the correct value of x. Similarly if we take 6 plus x equal to 3 then on subtracting 6 from both the sides of this equation we get value of x as minus 3. Again minus 3 does not lies between 0 and 9 so x cannot be equal to minus 3. Now let us take 6 plus x is equal to 6. Now on subtracting 6 from both the sides of this equation we get x is equal to 0. Now 0 represents a digit. So one possible value of x is 0. Now let us take 6 plus x equal to 9. Now on subtracting 6 from both the sides we get x is equal to 3. Now again this value of x lies between 0 and 9. So this is the another possible value of x. Now let us take 6 plus x equal to 12. Now subtracting 6 from both the sides of this equation we get value of x as 6. Again this value is lying between 0 and 9 so it is the another possible value of x. Now let us take 6 plus x equal to 15. Now 6 plus x is equal to 15 implies that x is equal to 9. Subtracting 6 from both the sides of this equation we get value of x as 9. Now this value is again lying between 0 and 9. So this is the another possible value of x. Here you can see from here that for other higher multiples of 3 value of x will be greater than 9. So these are the only possible values of x. Now we can write since x is a digit it can only be that 6 plus x is equal to 6 or 9 or 12 or 15. Now we can write therefore possible values of x are 0 or 3 or 6 or 9. Now let us check our answer. When x is equal to 0 then number becomes 240 and 80 multiplied by 3 is 240. So 240 is a multiple of 3. Now when x is 3 number becomes 243 and 3 multiplied by 81 is 243. So 243 is also a multiple of 3. Now when x is 6 then number is 246 and 3 multiplied by 82 is 246. So again 246 is a multiple of 3. Now when x is equal to 9 then number is 249 and 3 multiplied by 83 gives 249. So again 249 is a multiple of 3. So we can say thus x can have any of the 4 different values. So this is our required answer. This completes the session. Hope you understood the solution. Take care and bye for now.