A bucket of capacity 2000 mL is to be filled by using containers measuring 200 mL and 300 mL. Which one of the following combinations of containers is not correct for filling the bucket completely by the containers of 200 mL and 300 mL respectively?

The correct option/answer is 6, 3.

Step-by-step explanation:

Let $x$ be the number of 200 mL containers used and $y$ be the number of 300 mL containers used.

The total capacity of the bucket is 2000 mL. Therefore, we can write the equation as:

$200x+300y=2000$

Dividing the entire equation by 100 simplifies it to:

$2x+3y=20$

Now, let us test each given combination of $(x,y)$:

1. Combination 1, 6:

$2\left(1\right)+3\left(6\right)=2+18=20$

This gives exactly 2000 mL, so it is correct.

2. Combination 4, 4:

$2\left(4\right)+3\left(4\right)=8+12=20$

This gives exactly 2000 mL, so it is correct.

3. Combination 7, 2:

$2\left(7\right)+3\left(2\right)=14+6=20$

This gives exactly 2000 mL, so it is correct.

4. Combination 6, 3:

$2\left(6\right)+3\left(3\right)=12+9=21$

This gives 2100 mL, which does not equal 2000 mL.

Thus, the combination 6, 3 is NOT correct for filling the bucket completely.