The following sample questions are typical examples of the Analytical Reasoning problems you will find on the LSAT. There is a brief passage that presents a set of conditions, followed by questions about the relationships defined in the passage. While each passage among the examples here is followed by only one or two sample questions, each passage in the Analytical Reasoning section of the actual LSAT is followed by five to seven questions.
Directions:
Each group of questions in this section is based on a set of conditions. In answering some of the questions, it may be useful to draw a rough diagram. Choose the response that most accurately and completely answers the question and blacken the corresponding space on your answer sheet.
Passage for Question 1
A university library budget committee must reduce exactly five of eight areas of expenditure—G, L, M, N, P, R, S, and W—in accordance with the following conditions:
 If both G and S are reduced, W is also reduced.
 If N is reduced, neither R nor S is reduced.
 If P is reduced, L is not reduced.
 Of the three areas L, M, and R, exactly two are reduced.
Question 1
If both M and R are reduced, which one of the following is a pair of areas neither of which could be reduced?
 G, L
 G, N
 L, N
 L, P
 P, S
Explanation for Question 1
This question concerns a committee’s decision about which five of eight areas of expenditure to reduce. The question requires you to suppose that M and R are among the areas that are to be reduced, and then to determine which pair of areas could not also be among the five areas that are reduced.
The fourth condition given in the passage on which this question is based requires that exactly two of M, R, and L are reduced. Since the question asks us to suppose that both M and R are reduced, we know that L must not be reduced:
 Reduced: M, R
 Not reduced: L
The second condition requires that if N is reduced, neither R nor S is reduced. So N and R cannot both be reduced. Here, since R is reduced, we know that N cannot be. Thus, adding this to what we’ve determined so far, we know that L and N are a pair of areas that cannot both be reduced if both M and R are reduced:
 Reduced: M, R
 Not reduced: L, N
Answer choice (C) is therefore the correct answer, and you are done.
When you are taking the test, if you have determined the correct answer, there is no need to rule out the other answer choices. However, for our purposes in this section, it might be instructive to go over the incorrect answer choices. For this question, each of the incorrect answer choices can be ruled out by finding a possible outcome in which at least one of the two areas listed in that answer choice are reduced. Consider answer choice (A), which lists the pair G and L. We already know that for this question L must be one of the areas that is not reduced, so all we need to consider is whether G can be one of the areas that is reduced. Here’s one such possible outcome:
 Reduced: M, R, G, S, W
If areas M, R, G, S, W are reduced, then the supposition for the question holds and all of the conditions in the passage are met:
 M and R are both reduced, as supposed for this question.
 Both G and S are reduced, and W is also reduced, so the first condition is satisfied.
 N is not reduced, so the second condition is not relevant.
 P is not reduced, so the third condition is not relevant.
 Exactly two of L, M, and R are reduced, so the fourth condition is satisfied.
Thus, since G could be reduced without violating the conditions, answer choice (A) can be ruled out. Furthermore, since G appears in the pair listed in answer choice (B), we can also see that (B) is incorrect.
Now let’s consider answer choice (D), which lists the pair L and P. We already know that for this question L must be one of the areas that is not reduced, so all we need to consider is whether P can be one of the areas that is reduced. Here’s one such possible outcome:
 Reduced: M, R, P, S, W
If areas M, R, P, S, and W are reduced, then the supposition for the question holds and all of the conditions in the passage are met:
 M and R are both reduced, as supposed for this question.
 G is not reduced, so the first condition is not relevant.
 N is not reduced, so the second condition is not relevant.
 P is reduced and L is not reduced, so the third condition is satisfied.
 Exactly two of L, M, and R are reduced, so the fourth condition is satisfied.
Thus, since P could be reduced without violating the conditions, answer choice (D) can be ruled out. Furthermore, since P appears in the pair listed in answer choice (E), we can also see that answer choice (E) is incorrect.
This question was of moderate difficulty, based on the number of test takers who answered it correctly when it appeared on the LSAT. The most commonly selected incorrect answer choice was response (E).
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.
Question 2
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”:
1  2  3  4  5  6  7 
V 
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:
1  2  3  4  5  6  7 
V  U 
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:
1  2  3  4  5  6  7 
V  U  T  X  W  Y  Z 
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:
1  2  3  4  5  6  7 
V  U  T  X  W  Y  Z 
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.
Question 3
If U plays third, what is the latest position in which Y can play?
 first
 second
 fifth
 sixth
 seventh
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:
1  2  3  4  5  6  7 
T  V  U  X  W  Y  Z 
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:
1  2  3  4  5  6  7 
U  Y 
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.
Passage for Question 4
A charitable foundation awards grants in exactly four areas—medical services, theater arts, wildlife preservation, and youth services—each grant being in one of these areas. One or more grants are awarded in each of the four quarters of a calendar year. Additionally, over the course of a calendar year, the following must obtain:
 Grants are awarded in all four areas.
 No more than six grants are awarded.
 No grants in the same area are awarded in the same quarter or in consecutive quarters.
 Exactly two medical services grants are awarded.
 A wildlife preservation grant is awarded in the second quarter.
Question 4
If a wildlife preservation grant and a youth services grant are awarded in the same quarter of a particular calendar year, then any of the following could be true that year EXCEPT:
 A medical services grant is awarded in the second quarter.
 A theater arts grant is awarded in the first quarter.
 A theater arts grant is awarded in the second quarter.
 A wildlife preservation grant is awarded in the fourth quarter.
 A youth services grant is awarded in the third quarter.
Explanation for Question 4
This question deals with the awarding of grants during the quarters of a calendar year. As an aid in visualizing this problem, we can set up a simple table with columns representing the four quarters. Since the fifth condition in the passage states that “[a] wildlife preservation grant is awarded in the second quarter,” we know that all possible solutions for any question based on the passage must include a wildlife preservation grant awarded in the second quarter, which we can represent like this:
1  2  3  4 
W 
The particular question here begins with the added supposition that “a wildlife preservation grant and a youth services grant are awarded in the same quarter of a particular calendar year.” One possible way this could be satisfied is to have a youth services grant awarded in the second quarter in addition to the wildlife grant awarded in that quarter:
1  2  3  4 
W Y 
Another possibility would be to have a wildlife preservation grant and a youth services grant both being awarded in some quarter other than the second quarter. Given the condition that “[n]o grants in the same area are awarded in the same quarter or in consecutive quarters,” the only quarter in which a wildlife preservation grant could be awarded in addition to the second quarter is the fourth quarter. So the only alternative way to satisfy the added supposition is if both a wildlife preservation grant and a youth services grant are awarded in the fourth quarter:
1  2  3  4 
W 
W Y 
So far, then, we’ve determined that for this question there must be a youth services grant awarded in the second quarter or the fourth quarter.
Each of the incorrect answer choices for this question is a statement that could be true. The question asks you to identify the exception; that is, you need to find the statement that cannot be true. The correct answer choice is (E), which states: “A youth services grant is awarded in the third quarter.” This could not be true without violating the third condition, which specifies that “[n]o grants in the same area are awarded in the same quarter or in consecutive quarters.” We saw above that a youth services grant must either be awarded in the second quarter or the fourth quarter. On either possibility, awarding a youth services grant in the third quarter would result in two consecutive quarters where the youth services grant is awarded:
1  2  3  4 

W Y 
Y 
or:
1  2  3  4 
W  Y 
W Y 
In both cases, two youth services grants would be awarded in consecutive quarters, in violation of the third condition.
To see that each of the other answer choices could be true, it will suffice to construct a possible outcome for each one that is consistent with the supposition given in the question and the conditions in the passage. Consider the following possible outcome:
1  2  3  4 
T 
M W Y 
T  M 
A quick check of the conditions shows that this satisfies all of the conditions for the problem:
 A wildlife preservation grant and a youth services grant are awarded in the same quarter of a particular calendar year.
 Grants are awarded in all four areas. (The table includes at least one of each of the four letters—M, T, W, and Y.)
 No more than six grants are awarded. (The table contains exactly six entries.)
 No grants in the same area are awarded in the same quarter or in consecutive quarters. (In the table above, only T and M are repeated, and neither repetition appears in the same or consecutive columns.)
 Exactly two medical services grants are awarded. (The table contains exactly two M’s, in columns 2 and 4.)
 A wildlife preservation grant is awarded in the second quarter.
Notice that in this possible outcome, a medical services grant is awarded in the second quarter (answer choice (A)) and a theater arts grant is awarded in the first quarter (answer choice (B)). So answer choices (A) and (B) are both incorrect.
Now consider the following possible outcome:
1  2  3  4 
M 
T W 
M 
W Y 
A check of the conditions shows that this satisfies the supposition and all of the conditions. In this outcome, a theater arts grant is awarded in the second quarter (answer choice (C)) and a wildlife preservation grant is awarded in the fourth quarter (answer choice (D)). So answer choices (C) and (D) are also incorrect.
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 choice for this question was response (A).
Passage for Questions 5 and 6
From a group of seven people—J, K, L, M, N, P, and Q—exactly four will be selected to attend a diplomat’s retirement dinner. Selection conforms to the following conditions:
 Either J or K must be selected, but J and K cannot both be selected.
 Either N or P must be selected, but N and P cannot both be selected.
 N cannot be selected unless L is selected.
 Q cannot be selected unless K is selected.
Question 5
If P is not selected to attend the retirement dinner, then exactly how many different groups of four are there each of which would be an acceptable selection?
 one
 two
 three
 four
 five
Explanation for Question 5
This question adds a new supposition to the original set of conditions—“P is not selected to attend the retirement dinner.” The task is to determine all of the different possible selections that are compatible with this new supposition. A compatible solution is one that violates neither the new supposition nor the original conditions.
Since the second condition states “[e]ither N or P must be selected ...,” we can infer from the new supposition (P is not selected) and the second condition (either N or P, but not both, is selected) that N is selected. And since N is selected, we know from the third condition that L is selected. In other words every acceptable selection must include both L and N.
We are now in a good position to enumerate the groups of four which would be acceptable selections. The first condition specifies that either J or K, but not both, must be selected. So you need to consider the case where J (but not K) is selected and the case in which K (but not J) is selected. Let’s first consider the case where J (but not K) is selected. In this case, Q is not selected, since the fourth condition tells you that if K is not selected, then Q cannot be selected either. Since exactly four people must be selected, and since P, K, and Q are not selected, M, the only remaining person, must be selected. Since M’s selection does not violate any of the conditions or the new supposition, N, L, J, and M is an acceptable selection; in fact, it is the only acceptable selection when K is not selected. So far we have one acceptable selection, but we must now examine what holds in the case where K is selected.
Suppose that K is selected. In this case J is not selected, but Q may or may not be selected. If Q is selected, it is part of an acceptable selection—N, L, K, and Q. If Q is not selected, remembering that J and P are also not selected, M must be selected. This gives us our final acceptable selection—N, L, K, and M.
Thus there are exactly three different groups of four which make up acceptable selections, and (C) is the correct response.
This was a difficult question, based on the number of test takers who answered it correctly when it appeared on the LSAT.
Question 6
There is only one acceptable group of four that can be selected to attend the retirement dinner if which one of the following pairs of people is selected?
 J and L
 K and M
 L and N
 L and Q
 M and Q
Explanation for Question 6
The way in which this question is phrased is rather complex, and so it is important to get very clear what exactly is being asked. Unlike other questions which give you a new supposition to consider in conjunction with the original conditions, this question asks you to determine what is needed, in addition to the original conditions, to guarantee that only one group of four is acceptable.
One way to approach this question is to consider each option individually, and determine for each option whether only one acceptable group of four can be selected when the pair indicated in the option is selected. You may wish to vary the order in which the options are considered according to personal preferences. In the discussion here, we will consider the answer choices in order from (A) through to (E).
Choice (A): When both J and L are selected, K cannot be selected (first condition). Consequently Q cannot be selected (fourth condition). More than one group of four is acceptable under these circumstances, however: J, L, M, and N may be selected, and J, L, M, and P may be selected.
Choice (B): When K and M are both selected, J cannot be selected (first condition). Other than that, anyone else could be selected. This leaves more than one acceptable group of four. K, L, M, and N may be selected; K, L, M, and P may be selected; and K, M, P, and Q may be selected.
Choice (C): When L and N are both selected, P cannot be selected (second condition), but, as in the case of option (B), anyone else can be selected. This leaves more than one acceptable group of four: J, L, M, and N may be selected; K, L, M, and N may be selected; and K, L, N, and Q may be selected.
Choice (D): When L and Q are both selected, K must be selected (fourth condition). Consequently J cannot be selected (first condition). Either N or P must be selected (second condition), and there is nothing that rules out either N or P from being selected here. So, more than one group of four is acceptable under these circumstances: K, L, N, and Q may be selected, and K, L, P, and Q may be selected.
Choice (E): When M and Q are both selected, K must be selected (fourth condition), and hence J cannot be selected (first condition). Furthermore, N cannot be selected: if N were selected, then L would also have to be selected (third condition), and this would violate the restriction that exactly four people are to be selected. And since N cannot be selected, P must be selected (second condition). Thus when M and Q are both selected, both K and P must be selected as well, and only one group of four—K, M, P, and Q—is acceptable. (E) is therefore the correct response.
This was a very difficult question, based on the number of test takers who answered it correctly when it appeared on the LSAT.
Passage for Questions 7 and 8
On a particular Saturday, a student will perform six activities—grocery shopping, hedge trimming, jogging, kitchen cleaning, laundry, and motorbike servicing. Each activity will be performed once, one at a time. The order in which the activities are performed is subject to the following conditions:
 Grocery shopping has to be immediately after hedge trimming.
 Kitchen cleaning has to be earlier than grocery shopping.
 Motorbike servicing has to be earlier than laundry.
 Motorbike servicing has to be either immediately before or immediately after jogging.
Question 7
If laundry is earlier than kitchen cleaning, then hedge trimming must be
 fifth
 fourth
 third
 second
 first
Explanation for Question 7
This problem is concerned with determining the order in which six activities will be performed. As with many questions involving relative ordering or ranking, it is likely that you will find it useful to diagram the various relationships given in the passage.
The first condition in the passage tells us that grocery shopping has to be immediately after hedge trimming, which we can abbreviate as follows:
1. HG
The second condition tells us that kitchen cleaning has to be earlier than grocery shopping, which we can abbreviate as follows, where “...” is used to represent “earlier than” (which means any time before, including immediately before):
2. K ... G
The third condition tells us that motorbike servicing has to be earlier than laundry, and the fourth condition tells us that motorbike servicing has to be either immediately before or immediately after jogging. These conditions can be abbreviated as follows, where the / symbol is used to represent “or”:
3. M ... L
4. MJ / JM
Notice that the information specified in these four conditions can be collapsed into two ordering statements:
I. K ... HG (first and second conditions)
II. MJ / JM ... L (third and fourth conditions)
Question 7 introduces the new supposition “laundry is earlier than kitchen cleaning”:
L ... K
This new supposition works to further collapse the ordering statements in I and II to the single statement below; that is, if L must be earlier than K, then we know that the activities must be ordered like this:
MJ / JM ... L ... K ... HG
So, with the addition of the new supposition, there are exactly two possible orderings of the six activities, differing only with respect to whether motorbike servicing is immediately before or immediately after jogging:
1  2  3  4  5  6 
M  J  L  K  H  G 
J  M  L  K  H  G 
Question 7 asks what position hedge trimming must be in, given the new supposition. What we see here is that hedge trimming must be the fifth activity performed, and so answer choice (A) is correct.
This was an easy 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 response (B) and response (C).
Question 8
Which one of the following, if substituted for the condition that motorbike servicing has to be earlier than laundry, would have the same effect in determining the order of the student’s activities?
 Laundry has to be one of the last three activities.
 Laundry has to be either immediately before or immediately after jogging.
 Jogging has to be earlier than laundry.
 Laundry has to be earlier than hedge trimming.
 Laundry has to be earlier than jogging.
Explanation for Question 8
This question asks you to select the condition which, if substituted for the third condition in the passage (repeated below), would have the same effect as the original condition.
Third condition: Motorbike servicing has to be earlier than laundry.
In this case, you can deduce that the correct answer choice is (C):
(C) Jogging has to be earlier than laundry.
The fourth condition in the passage tells you that motorbike servicing has to be either immediately before or immediately after jogging. That is, M and J must be ordered as a block, either MJ or JM, with respect to the other four activities. Thus, if, as the original third condition states, M has to be earlier than L, then we know that J must also be earlier than L. Conversely, if, as the new condition in answer choice (C) states, J has to be earlier than L, then we know that M must also be earlier than L. In short, the third condition and answer choice (C) have exactly the same effect. Therefore, answer choice (C) is correct.
Another way to approach this kind of question is to attempt to eliminate all of the incorrect answer choices. Under this approach, you want to rule out any answer choice that does either of the following:
 rules out outcomes that the original condition allows
 allows outcomes that the original condition rules out
Let’s see how this approach would enable us to eliminate answer choices (A), (B), (D), and (E).
Consider the condition presented in answer choice (A):
(A) Laundry has to be one of the last three activities.
We can first ask whether this condition would rule out outcomes that the original third condition allows. To answer this question, we must simply determine whether there is an outcome allowed by the original third condition along with the other conditions in which laundry is one of the first three activities. Here is such an outcome:
1  2  3  4  5  6 
M  J  L  K  H  G 
Because the original third condition allows this outcome, but the condition in answer choice (A) does not, answer choice (A) cannot be correct.
Consider answer choice (B):
(B) Laundry has to be either immediately before or immediately after jogging.
Again, we want to first determine whether this new condition would rule out outcomes that the original third condition allows. To answer this question, we must simply determine whether there is at least one outcome allowed by the original third condition along with the other conditions in which laundry is neither immediately before nor immediately after jogging. Here is one such outcome:
1  2  3  4  5  6 
K  H  G  J  M  L 
This outcome, although allowed by the original third condition, would be ruled out by the alternative condition given in answer choice (B). Thus, answer choice (B) cannot be correct.
Next consider answer choice (D):
(D) Laundry has to be earlier than hedge trimming.
Again, we want to first determine whether this new condition would rule out outcomes that the original third condition allows. To answer this question, we must simply determine whether there is at least one outcome allowed by the original third condition along with the other conditions in which laundry is not earlier than hedge trimming. One such outcome was given immediately above: since L is not earlier than H in this outcome, it would be ruled out by the condition in answer choice (D). So, answer choice (D) rules out an outcome that the original third condition allows, and therefore (D) cannot be the correct answer choice.
Finally, consider answer choice (E):
(E) Laundry has to be earlier than jogging.
Again, we want to first determine whether having this new condition would rule out outcomes that are allowed when the original third condition is in place. To answer this question, we must simply determine whether there is at least one outcome allowed by the original third condition along with the other conditions in which laundry is not earlier than jogging. One such outcome was given above: since L is not earlier than J in this outcome, it would be ruled out by the condition presented in answer choice (E). So, answer choice (E) rules out an outcome that the original third condition allows, and therefore (E) cannot be the correct answer choice.
In sum, answer choices (A), (B), (D), and (E) can all be eliminated because in each case the condition is one that rules out outcomes that the original condition allows. For this particular question, there was no need to consider whether any of the options could be eliminated because they allowed outcomes that the original condition ruled out.
This question was of middle difficulty, 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 response (A) and response (B).