13) E

Instead of going straight into the answer, let us examine each of the options given.

A – Wrong (1 and 2)
Even if both bags each started off with more than two marbles, it would still be possible to obtain the results that we got. 1 marble from the left bag was put into the right bag and then one from the right bag was put into the left. A is wrong.

B – Wrong (1 and 3)
Let us say the left bag starts 4 marbles in and all of them were green.
Let us say that the right bag starts 2 (both red) marbles.
If one green was taken from the left bag and placed in the right bag and then one red from the right bag was placed in the left, we can still obtain the results that we did. B is wrong.

C – Wrong (1 and 4)
Let us say the left bag starts 4 marbles in (2 green, 2 red)
Let us say the right bag starts with 2 red marbles.
If one green was taken from the left bag and placed in the right bag and then one red from the right bag was placed in the left, we can still obtain the results that we did. C is wrong.

D – Wrong (2 and 3)
Let us say the left bag starts 4 marbles in (4 green)
Let us say the right bag starts with 4 marbles. (2 red, 2 green)
If one green was taken from the left bag and placed in the right bag and then one green from the right bag was placed in the left, we can still obtain the results that we did. (Right can have 2 green and 2 red). D is wrong.

E – Correct (2 and 4)
Let us say the left bag starts 2 marbles in (1 green, 1 red) [It doesn’t matter how many there are in the left]
Let us say the right bag starts with 4 marbles. (4 red) [more than 2 and same colour]
If one green was taken from the left bag and placed in the right bag and then one red from the right bag was placed in the left, we cannot obtain the results that we did. There won’t be half green and half red. E is correct.

F – Wrong (3 and 4)
Let us say the left bag starts 2 marbles in (2 green) [same colour]
Let us say the right bag starts with 2 marbles. (2 red) [same colour]
If one green was taken from the left bag and placed in the right bag and then one red from the right bag was placed in the left, we can obtain the results that we did. There will be half green and half red in the right bag. F is wrong.