Answer B

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.