#13 - Global, Must Be True

[Administrator]

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=6962)

The correct answer choice is (D)

The question asks us to determine a pair of variables of which at least one must be selected. There are many such pairs, unfortunately, making prephrasing the answer somewhat complicated. We know, for instance, that at least one of F or G must be selected; however, this is not a pair in any of the answer choices.

At this point, many students would resort to the tried-and-true plug-and-chug approach: eliminate both variables from each answer choice, and test if the resulting selection violates any of the rules. If it does, then the answer choice contains a pair of variables of which at least one must be selected, validating the correct answer choice. While logically sound, this approach would be laborious and woefully inefficient. There is (almost always) a more efficient way to proceed.

Recall our earlier discussion of three key variables—O, P, and W. We observed that eliminating any one of them would determine to a large extent which variables must be selected:

Well, if eliminating any one of these three variables represents such a strong point of restriction, it would be wise to focus your attention on those answer choices that include at least one of O, P, or W. Indeed, answer choice (D) includes two of them—O and P—making it a reasonable first stop. A quick glance at either of our two inferences reveals that if O is not selected, then the selection of variables must include P. The same conclusion can be drawn about O if P is not selected. Thus, either O or P—or both—must always be selected.

Answer choice (A): This answer choice is incorrect, because we do not need to select either F or T. Since F and T are both hot foods, without either of them we would need to select N in compliance with the second rule. N and V cannot both be selected (fifth rule), forcing V out. The remaining five variables can be selected without violating any of the rules:

PT65_D11 LG Explanations_game_#3_#13_diagram 1.png

Answer choice (B): This answer choice is incorrect, because we do not need to select either G or O. According to the contrapositive of the fourth rule, if O is not selected, G cannot be selected. The resulting selection of variables (F, T, P, W, N/V) violates none of the rules, suggesting that G and O can both be eliminated without issue.

Answer choice (C): This answer choice is incorrect, because we do not need to select either N or T. Since N and T are both hot foods, without either of them we would need to select F in compliance with the second rule:

PT65_D11 LG Explanations_game_#3_#13_diagram 2.png

With two of the three spaces in the “unassigned” group filled, P and W cannot both be excluded. Consequently, the third rule would require that we select both P and W:

PT65_D11 LG Explanations_game_#3_#13_diagram 3.png

With only three variables remaining—G, O, and V—recall the fourth rule and its contrapositive: if O is not selected, then G cannot be selected. There is no space for both O and G in the “unassigned” group, which is why O must be selected:

PT65_D11 LG Explanations_game_#3_#13_diagram 4.png

It’s worth repeating that this analysis merely explains why a given answer choice is incorrect, and is given for informational purposes only. If you approached this question correctly (as described above), there would be no reason to worry about whether at least one of N or T must be selected.

Answer choice (D): This is the correct answer choice, as described above. Without O and P, we would be forced to also exclude G (by the contrapositive of the fourth rule), as well as W (third rule). This would prevent us from selecting five of the eight available variables, violating the numerical premise in the scenario. Therefore, at least one of O or P must be selected.

Answer choice (E): This answer choice is incorrect, because a working solution does not require us to select either V or W. If neither were selected, we would need to also exclude P, in accordance with the third rule. The remaining five variables can all be selected without violating any of the rules:

PT65_D11 LG Explanations_game_#3_#13_diagram 5.png

[cls]

Hi, I was hoping to get some insight about this game. I recognized this game as a Linear game, but after grading the test I realized it's classified as a grouping game. I'm not sure exactly how this should have impacted my diagraming (I had a 1-5 base and I did realize that there were three different categories for the varibles). Question 13 is the only one I missed. I had a hard time figuring out how to efficiently solve this question in a reasonable amount of time. Might anyone be bake to shed some light in this game?

Thanks.

[Jon Denning]

Hey cls,

Thanks for the question! This is a tricky game because it at first feels Linear, but as you consider the rules (conditional), questions (nothing about order), and answer choices it becomes clear that you're really just constructing five-item groups based on the eight food options and their characteristics. The only real impact this has on diagramming is that 1-5 isn't necessary for the base; just have five spaces for your "in" group and three for your "out" group.

At that point it's just a matter of being diligent about classification of foods by type (dessert, main, side) and temp (hot or not).

Let's look at 13:

13. The key here is thinking about the consequences if both foods for each answer weren't selected, i.e. both were "out." For the correct answer that will cause a problem, since we know that at least one of the two must be "in." Of course, from the last rule we know that at least one of N and V must always be out, so only two open spaces remain for our "out" group, and that's going to be a critical idea.

(A) If F and T are both out, then our "in" group is: G, O, P, W, N/V. That satisfies
our rules so we don't have to select F or T.

(B) If G and O are both out, then our "in" group is: F, P, T, W, N/V. That satisfies
our rules so we don't have to select G or O.

(C) If N and T are both out, then our "in" group is: F, P, W, O, G/V. That satisfies
our rules as well, so we don't have to select N or T.

(D) If O and P are both out, then our "in" group is: F, G, T, W, N/V. What's wrong
with this arrangement? We have G, but no O. That violates the fourth rule of
G O, so we can never have O and P out together. At least one must
be selected.

(E) If V and W are both out, then our "in" group is: F, G, N, O, T. Again, another
valid possibility.

So the key to this question was moving VERY quickly through the answer choices looking at the consequences of removing both foods together and waiting until a clear violation appeared. That's the correct answer.

I hope this helps!

[cls]

Hi Jon,

I neglected to use the "in" and "out" approach which makes a world of a difference. I was trying to see which variable had to be "in" and that provd overwhelming, especially considering many of variables were repeated throughout the answer choices.

Thanks for explaining!

[Jon Denning]

No problem! I always encourage people to think about both groups (in and out) when you're dealing with an Overloaded--more variable available than are being selected--game. The test makers are notorious for testing the selected group via the out group, and vice versa.

[swimmingly]

Hi,

This is my first time posting in the forum, but I did review the other forums on this specific lsat game before posting my question here.

I have a question regarding how to arrive at the correct answer choice for Question 13 in the December 2011 logic games. Get comfy, this question has a prologue

I understood the basic rules and came up with the correct diagram but I had some difficulties drawing out all of the correct inferences in order to make the game a home run--I got question 13 and 16 wrong. As I am reviewing the correct answer choice and trying to reverse engineer how one would arrive at the correct response for question 13 I don't seem to be able to fully get there. My suspicion is that it is that I am not fully understanding the nature of the relationship, and subsequent inferences, between o and g in this question.

So (sorry this is kinda long), I believe rule and inference diagram would be:
(~ represents 'not')
G --> O and ~O --> ~G

But can the inference be made then O --> G? Because I believe that is the inference that I am not getting (and not only on this question, but on other games too). If that is the case, could you please explain when and how I am able to make that inference? If not, it would be great if you could kindly direct me to the boat that I missed Thank you!

[Jon Denning]

Hey swimmingly,

Thanks for the question, and welcome to the Forum!

I know this game, and this question, well, so I'm happy to help you out and feel like we can get this sorted without too much trouble

Question 13 is an oddly-worded one—which is a pair of which at least one must be selected?—but really what it's asking you is, "which of the following pairs has two foods that can never both be out?" In other words, if at least one must always be selected, then it's impossible for both to be not selected...you can test answers by simply removing both and seeing if it could work!

So when we work through the answers and arrive at the correct choice, (D), we can test it by seeing what would happen if both O and P were both out:

If O is out then G is also out (contrapositive of the rule you mention). And of course with G out then F is in, since at least one Dessert must be selected. That doesn't matter here, turns out, but so far so good...

If P is out then W must also be out, based on the rule that if one is in they must both be (this is a double-arrow, as is the contrapositive: P W).

So now we're missing O, G, P, and W. We started with 8 foods and had to select exactly 5, but we've just removed 4! We only have 4 left to select, then, and that's the violation caused by (D).

To your other question about O G: NO! We only know what happens when G is selected (rule), and when O is not selected (contrapositive). Going from O to G is a Mistaken Reversal and must be avoided at all costs! So if you find yourself falling victim to that in other games please, PLEASE spend some time correcting it: it's by far the most common trap the test makers use.

I hope this helps!

Jon