Put a digit in the gap, such that the answer is a whole number:

3x+486=100 ...

What are all the possible digits?

Answer: The possible digits are 2,5 and 8

Step-by-step explanation:

3x + 486 = 100_

From the equation in the question, we are looking for a digit to put in the gap after 100 to make sure that when we solve the question, x will be a whole number.

Therefore, since it's a single digit required, the possible digits will be from 0 to 9.

Now, from divisibilty tests, for a number from 2 digits upwards to be divisible by 3, the sum of its digits has to be divisible by 3.

Going back to the question, let's divide each term by 3 to get;

3x/3 + 486/3 = 100_ to give;

x + 162 = 100_ / 3

Now for x to be a whole number, the value on the right hand side must be a whole number.

Therefore, since we know that for a 2 digits and above number to be divisible by 3, it's sum must be divisible by 3. We can plug in any of the digits from 0-9 into the gap and add up.

For 0; 1+0+0+0 = 1

For 1; 1+0+0+1 = 2

For 2; 1+0+0+2 = 3

Following the same addition pattern for digits 3,4,5,6,7,8and 9, we'll get sum of 4,5,6,7,8,9 and 10 respectively.

Inspecting the above, the only additions that are divisible by 3 are when the digit is; 2,5 and 8