#15 - Global, Must Be True, Maximum

[Dave Killoran]

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=14120)

The correct answer choice is (C)

You know from question #13 that you can have at least three members in group F, so answer choice (A) is immediately incorrect. And you know from rules 3 and 4 that at least two people must be separated from the others (at least two spaces in each group to account for the separation of W/Z and U/G), so the maximum at this point could only be five (answer choice (E) is incorrect). Five will not work either though, because H and G cannot be in F together, so answer choice (D) is incorrect. Looking at Inference 3 you see that Z, H, and U can all be in committee F, and G, L, and W are then in I. Only M is unaccounted for. Can M go in committee F in this scenario? Yes, since there is nothing preventing M from being in F. So that makes a maximum of 4 members possible, and the correct answer is (C).

[baxleyce]

This question tripped me up due to the timing of figuring it out. Is this a question where the 3rd inference is crucial to finding the correct answer? I didn't have that inference written down and got all the questions correct except for this one. What is the best strategy with minimum/maximum questions? Thanks!

[Robert Carroll]

Baxley,

I have a huge chain of conditionals for this one:

L(f) U(i) G(f) H(i) Z(i) W(f)

Also, below the first arrow, L(f) M(i)

Inference-wise, because we have two pairs of variables that conflict with each other, each group has at least 2 members. So we try to maximize Finance, noting that if L is in Finance, the huge chain tells me that Finance has exactly 3 members. So, we certainly can make Finance have a size of 3; the only way to get it bigger is to try to leave L out of Finance. So L is in Incentives, and Incentives now has 3 people: L, one of G, U, one of W, Z. Note what we know so far: Finance could be 3 people (with L, for sure) and never more than 4 (because, with L not there, we have at least 3 people already in Incentives). So only two answers are even viable at this point: answer choice (B) and answer choice (C). If we can construct a situation where Finance has 4 people, none of whom can be L, we'll prove it's answer choice (C).

Such a situation can be done:

Finance: ZHUM

Incentives: LGW

For min/max questions in general, looking at previous work can often help to prove that some things DO work. If I've created a situation where 3 people can be in Finance, I certainly know that 2 is not the max. Double-Not Arrows also limit group size, because they prevent variables from being together. A theoretical limit of 5 for each group already exists because of the inferences from the 3rd and 4th rules in this game, for instance. Before brute-forcing situations to try to create a maximum, look at what you've done before and what general limitations on size exist, without looking at specific variables at the outset. That should limit the size somewhat on its own, and you can then create hypotheticals within those more restricted parameters.

Robert Carroll

[baxleyce]

Baxley,

I have a huge chain of conditionals for this one:

L(f) U(i) G(f) H(i) Z(i) W(f)

Also, below the first arrow, L(f) M(i)

Inference-wise, because we have two pairs of variables that conflict with each other, each group has at least 2 members. So we try to maximize Finance, noting that if L is in Finance, the huge chain tells me that Finance has exactly 3 members. So, we certainly can make Finance have a size of 3; the only way to get it bigger is to try to leave L out of Finance. So L is in Incentives, and Incentives now has 3 people: L, one of G, U, one of W, Z. Note what we know so far: Finance could be 3 people (with L, for sure) and never more than 4 (because, with L not there, we have at least 3 people already in Incentives). So only two answers are even viable at this point: answer choice (B) and answer choice (C). If we can construct a situation where Finance has 4 people, none of whom can be L, we'll prove it's answer choice (C).

Such a situation can be done:

Finance: ZHUM

Incentives: LGW

For min/max questions in general, looking at previous work can often help to prove that some things DO work. If I've created a situation where 3 people can be in Finance, I certainly know that 2 is not the max. Double-Not Arrows also limit group size, because they prevent variables from being together. A theoretical limit of 5 for each group already exists because of the inferences from the 3rd and 4th rules in this game, for instance. Before brute-forcing situations to try to create a maximum, look at what you've done before and what general limitations on size exist, without looking at specific variables at the outset. That should limit the size somewhat on its own, and you can then create hypotheticals within those more restricted parameters.

Robert Carroll

Thank you, Robert, that helped!