We know that there are seven judges - two are conservative, two are moderate, and three are liberal. C, C, M, M, L, L, L
Each judge voted for or else against granting the petition.
FOR: _ _ _ _ _ _ _ AGAINST: _ _ _ _ _ _ _
Now let's go through the conditions.
Rule 1 - If the two Cs and at least one L voted the same way as each other, then both Ms voted that way.
Rule 2 - If the three Ls voted the same way as each other, then no C voted that way.
Rule 3 - At least two judges voted for and at least two voted against.
Rule 4 - At least one C voted against.
Scenario (A):
Rule 1 and 4 working together mean that the scenario outlined in Rule 1 could only occur if both Cs voted against
FOR: L L AGAINST: C C L M M
We also know that at least two voted for; therefore, the remaining two Ls must have voted for in this scenario. This scenario could not work if the variables were flipped as at least one C voted against.
Scenario (B):
Rules 2 and 4 working together mean that the three Ls could only vote the same way if they vote for.
FOR: L L L AGAINST: C C
It doesn't matter whether the Ms vote for or against in this scenario.
Another inference we can make:
Overall, at least one L must vote for the petition as all three Ls voting against would mean that no C could vote against, violating Rule 4.
Now that we've gone through some possible scenarios and made some inferences, let's address the question stem. If exactly two judges voted against, which must be true?
We know that at least one C must vote against.
If one M voted against, then all three Ls would have to vote for. This would mean that the remaining C would have to vote against, violating the new condition imposed by the question stem:
FOR: L L L AGAINST: C M C
Therefore, both Ms must have voted for.
There are two possible ways this could occur.
Scenario (1)
FOR: L L L M M AGAINST: C C
Scenario (2)
FOR: L L C M M AGAINST: C L
These two scenarios and the original conditions eliminate all other possible answers.
We can eliminate answer choice (C) because we know that at least one C voted for.
We can eliminate answer choices (B) and (D) because they are disproved by Scenario (1) outlined immediately above.
We can eliminate answer choice (E) because it is disproved by Scenario (2) outlined immediately above.
Hope this helps! Please let us know if you have any further questions.
