Passage for Questions 2 and 3
Seven piano students—T, U, V, W, X, Y, and Z—are to give a recital, and their instructor is deciding the order in which they will perform. Each student will play exactly one piece, a piano solo. In deciding the order of performance, the instructor must observe the following restrictions:
X cannot play first or second.
W cannot play until X has played.
Neither T nor Y can play seventh.
Either Y or Z must play immediately after W plays.
V must play either immediately after or immediately before U plays.
If V plays first, which one of the following must be true?
T plays sixth.
X plays third.
Z plays seventh.
T plays immediately after Y.
W plays immediately after X.
Explanation for Question 2
This question deals with an ordering relationship defined by a set of conditions concerning when seven piano students will perform. As an aid in visualizing this problem you can draw a simple diagram that shows the seven recital slots arranged in order from left to right. Student V is shown in the first slot, as specified by the supposition that “V plays first”:
We can immediately fill in one of the empty slots in the diagram. The condition that “V must play either immediately after or immediately before U plays” tells us that U must occupy the second slot in the recital schedule. This is shown below:
Since the question asks us what must be true, we can eliminate incorrect responses by showing that they could be false. Response (A) is incorrect because the statement that “T plays sixth” is not necessarily true—we can place T in one of the slots other than sixth and still meet all the conditions of the problem. One such recital schedule, with T playing third, is shown in the diagram below:
This schedule can be derived as follows:
With V, U, and T in the first three positions, there are four positions left for W, X, Y, and Z.
W must come after X—because of the condition that “W cannot play until X has played”—so if X is fourth and W is fifth, this condition will be met.
This leaves two possible slots for Y and Z. Y cannot play seventh because of the condition that “Neither T nor Y can play seventh.” Suppose, then, that Y is sixth and Z is seventh.
A check will verify that this schedule meets the conditions of the problem, including the one that “Either Y or Z must play immediately after W plays.”
The schedule shown in the diagram also demonstrates that response (B) is incorrect. In it, X plays fourth, so it is not correct that the statement, “X plays third,” must be true.
Response (C), “Z plays seventh,” is the credited response. We can show Z must be seventh by demonstrating that:
all the conditions can be met with Z in the seventh slot, and
some of the conditions would be violated with Z in any slot other than seventh.
To demonstrate that Z can play seventh, you can refer to the schedule that was developed for the discussion of response (A), above. In it, Z plays seventh, and the supposition given in the question and all the conditions in the passage are met.
To demonstrate that Z cannot play in a slot other than seventh, we can attempt to find another student to play seventh. We already know that neither U nor V can play seventh. Hence, there are four remaining players: T, W, X, and Y. However, a review of the conditions shows that none of those players can play seventh:
The third condition states that “Neither T nor Y can play seventh.”
W can’t play seventh, because there must be a slot following W’s in order to meet the condition, “Either Y or Z must play immediately after W plays.” If W plays seventh, then there is no such slot left for Y or Z.
For a similar reason X can’t play seventh, because there must be a slot following X’s in order to meet the condition, “W cannot play until X has played.”
Since Z can play seventh and no other player can, then the statement that Z must play seventh is correct and (C) is the credited response.
Response (D) is incorrect because it is not necessarily true that “T plays immediately after Y.” In our discussion of response (A), we developed a schedule in which T plays third and Y plays sixth, yet all conditions are satisfied.
Response (E) is incorrect because, as shown in the diagram below, it is not necessarily true that “W plays immediately after X.” This schedule is obtained by simply reversing the order of players W and Y in the schedule we developed in the analysis of response (A).
A review will show that all of the suppositions given in the question and all the conditions in the passage are met by this schedule:
This was a difficult question, based on the number of test takers who answered it correctly when it appeared on the LSAT. The most commonly selected incorrect answer choices were (B) and (E). In answering this question, it is important to derive information not explicitly mentioned in the passage, such as that W cannot perform seventh.
If U plays third, what is the latest position in which Y can play?
Explanation for Question 3
This question involves the same original conditions as the previous problem, but it begins with an additional supposition: “U plays third.” You must determine what effect this supposition would have on the possible positions in which Y can appear in the recital schedule.
The correct response is (D): Y can play as late as sixth. The diagram below shows a recital order that meets all the conditions and has Y performing in the sixth position:
One strategy for arriving at this solution is to work backward to see which position is the latest in which we can place Y and at the same time produce a recital schedule that meets all the conditions.
Using that approach, we immediately see that Y cannot play as late as seventh, because of the condition that “Neither T nor Y can play seventh.” Backing up and placing Y sixth, we can begin to fill in the schedule, as follows:
This schedule has five empty slots, into which we must fit players T, V, W, X, and Z. The following is a series of reasoning steps that can be used:
From our analysis of the previous question, we know that players T, W, and X cannot play seventh, but that Z can, so we can tentatively place Z in the seventh slot.
We also know that “Either Y or Z must play immediately after W plays.” If we place W in the fifth slot, this condition will be met.
By placing V in the second slot, we can meet the condition that “V must play either immediately after or immediately before U plays.”
We must place the remaining two players, T and X, in the two remaining slots, the first and the fourth. Because the first condition states that “X cannot play first ...,” we will place X in the fourth slot and T in the first. These positions will meet the conditions that apply to T and X: T will avoid playing seventh and X will play before W.
Since Y can play as late as sixth, response (D) is the correct solution.
This question was of middle difficulty, based on the number of test takers who answered it correctly when it appeared on the LSAT.