The hobbyist could select any of the following plant combinations EXCEPT

Victoria on April 17, 2021

Hi @eversm,

Happy to help!

We know that a hobbyist is stocking her aquarium with exactly three fish of different types and exactly two species of plants.

The options for fish are: G, H, J, K, and L. This means that three fish will be "in" and two will be "out."

The options for plants are: W, X, Y, and Z. This means that two plants will be "in" and two will be "out."

Fish: _ _ _ | _ _
Plants: _ _ | _ _

Now let's go through our conditions.

Rule 1 - if she selects the G, then she can select neither the H nor a Y

G --> Not H AND Not Y
H OR Y --> Not G

Rule 2 - she cannot select the H unless she selects the K

H --> K
Not K --> Not H

Rule 3 - she cannot select the J unless she selects a W

J --> W
Not W --> Not J

Rule 4 - if she selects the K, she must select an X

K --> X
Not X --> Not K

We can combine Rules 2 and 4 to conclude H --> K --> X (and Not G) as well as Not X --> Not K --> Not H

Therefore, if X is not selected, then H and K cannot be selected. This means that G, J, and L must be the fish in the tank.

We know that, if J is selected, W must be selected. We also know that, if G is selected, Y cannot be selected. Therefore, in this scenario, our three fish would be G, J, and L and our two plants would be W and Z. This means that answer choice (C) could be true and is therefore incorrect.

Scenario 1
Fish: G J L | H K
Plants: W Z | X Y

There are no rules directly involving Z so let's examine this next. We already know that W and Z can be stocked together. What about X and Z?

If our two plant species are X and Z, then W is not selected. Therefore, J cannot be selected. We also know that G and H cannot be stocked together. So let's try stocking H, K, and L.

Scenario 2
Fish: H K L | G J
Plants: X Z | W Y

This meets all of our rules. H is stocked and G is not. H, K, and X are stocked and neither J nor W is stocked. Therefore, answer choice (E) is also incorrect.

Now that we have this set-up, what if we swap the Z and the W?

Scenario 3
Fish: H K L | G J
Plants: X W | Z Y

This also meets all of our rules. H is stocked and G is not. H, K, and Z are stocked. J is not stocked, but it does not have to be even if W is stocked. Therefore, answer choice (A) is also incorrect.

This leaves us with answer choices (B) and (D).

We could make an easy swap under Scenario 2 to eliminate answer choice (D). There are no rules directly involving Z, so we can swap it for Y. Again, all of our rules are met. H and Y are stocked, and G is not. H, K, and Z are stocked and neither J nor W is stocked.

Scenario 4
Fish: H K L | G J
Plants: X Y | W Z

This means that answer choice (B) is our correct answer. But why? If we select Y, then G cannot be stocked. We cannot stock X; therefore, neither H nor K can be stocked based on Rules 2 and 4. However, this doesn't leave us with enough fish. We can only stock J and L and we need to stock three fish. Therefore, W and Y cannot be stocked together.

Hope this helps! Please let us know if you have any further questions.