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Sample Logic Game

Logic Games appear in the analytical reasoning section of the Law School Admissions Test (LSAT)

On the LSAT, four logic games must be completed in 35 minutes, giving just a bit more than 8 and a half minutes to finish each game.

The game shown here is an ordering game (grouping games, matching games, and spatial games also appear on the LSAT) and is generally considered an easier game.

If you wish to time yourself, you may use the stopwatch at the top of the game. You can view whether an answer is correct or incorrect by clicking on it (a short explanation will also appear)(Javascript must be enabled in order to use the timer or click the answers). A full answer key appears at the bottom, along with an in-depth set-up and explanation for the game.



An advertising executive must schedule the advertising during a particular television show. Seven different consecutive time slots are available for advertisements during a commercial break, and are numbered one through seven in the order that they will be aired. Seven different advertisements B, C, D, F, H, J, and K must be aired during the show. Only one advertisement can occupy each time slot. The assignment of the advertisements to the slots is subject to the following restrictions:
B and D must occupy consecutive time slots.
B must be aired during an earlier time slot than K.
D must be aired during a later time slot than H.
If H does not occupy the fourth time slot, then F must occupy the fourth time slot.
K and J cannot occupy consecutively numbered time slots.


1.Which of the following could be a possible list of the
advertisements in the order that they are aired?
(A) BDFHJCK
(B) CJBHDKF
(C) HBDFJCK
(D) HDBFKJC
(E) HJDBFKC

2. If advertisement B is assigned to the third time slot, then which
of the following must be true?
(A) C is assigned to the sixth time slot.
(B) D is assigned to the first time slot.
(C) H is assigned to the fourth time slot.
(D) J is assigned to the fifth time slot.
(E) K is assigned to the seventh time slot.

3. Which of the following could be true?
(A) B is assigned to the first time slot.
(B) D is assigned to the fifth time slot.
(C) H is assigned to the seventh time slot.
(D) J is assigned to the sixth time slot.
(E) K is assigned to the third time slot.

4. If C is assigned to the third time slot, then each of the
following could be true EXCEPT:
(A) B is assigned to the fifth time slot.
(B) D is assigned to the sixth time slot.
(C) F is assigned to the fourth time slot.
(D) J is assigned to the first time slot.
(E) K is assigned to the second time slot.

5. If H is assigned to the first time slot, then which of the
following is a complete and accurate list of all the time slots
to which C could be assigned?
(A) second, fifth, sixth, seventh
(B) second, fourth, fifth, sixth, seventh
(C) second, fourth, sixth
(D) second, third, fifth, sixth, seventh
(E) second, third, sixth

6. If J is assigned to the seventh slot, then which of the
following must be assigned to the fifth slot?
(A) B
(B) C
(C) D
(D) F
(E) K




















Answer to Question 1: C   Explanation for Question 1
Answer to Question 2: A   Explanation for Question 2
Answer to Question 3: B   Explanation for Question 3
Answer to Question 4: E   Explanation for Question 4
Answer to Question 5: E   Explanation for Question 5
Answer to Question 6: E   Explanation for Question 6

The Setup
To begin solving the game, you should draw 7 dashes to represent the seven possible time slots for the advertisements and make a note of the seven advertisements that will fill the slots, as shown:


B C D F H J K


 1      2      3      4      5      6      7    



Now you'll want to make a quick visual representation of each rule, so you can see how the advertisements could fit into the spots.

Rule #1: BD or DB
Rule #2: B -- K
Rule #3: H -- D
Rule #4: 4 = F or H
Rule #5: JK and KJ
B C D F H J K


                    
1 2 3 4 5 6 7



Before moving on to the questions, take a moment to combine together the information and place anything you can into your picture.

Rules 1, 2, and 3 can be combined: (The small triangle above the B and D indicates that they can switch places.)
Rule #4 can be placed into the picture.
B C D F H J K


         F/H         
1 2 3 4 5 6 7


You should note that if H is chosen for slot 4, then B,D,and K will have to follow in slots 5, 6, and 7 (B and D can, of course, switch slots with one another.)
If, instead, F is selected for slot 4, then B and D will have a choice of either being placed into slots 2 and 3 or else into slots 5 and 6.


Question 1
Question 1 is a simple list question. To answer it, simply compare each rule to the answer choices, and cross off any choice that violates the rule.

Rule #1: BD or DB
Rule #2: B -- K
Rule #3: H -- D
Rule #4: 4 = F or H
Rule #5: JK and KJ
Answers:
(A) B D F H J C K
(B) C J B H D K J
(C) H B D F J C K
(D) H D B F K J C
(E) H J D B F K C


Rule #1 is violated by answer choice B, so B cannot be correct.
Rule #2 is not violated by any choice.
Rule #3 is violated by answer choice A, so A cannot be correct.
Rule #4 is violated by answer choice E, so E cannot be correct.
Rule #5 is violated by answer choice D, so D cannot be correct.
This leaves only answer choice C, which must be the correct answer.

This scenario can now be used to answer other "could be true" questions!


Question 2
To solve this question, you should begin by redrawing your picture and placing B into slot 3.

      B F/H         
1 2 3 4 5 6 7

D must be adjacent to B, so it must be in slot 2, which means that H must be in slot 1.

H D B F/H         
1 2 3 4 5 6 7


F must occupy slot 4, since H now occupies slot 1. This leaves only C, J, and K for the remaining three empty spaces.

H D B F         
1 2 3 4 5 6 7


Since J and K cannot be next to each other, they must separate into slots 5 and 7, leaving C for slot 6.
H D B F J/K C K/J
1 2 3 4 5 6 7


This means that C must be in 6, which is answer choice A.


Question 3
This question is fairly simple if you took the time to combine rules 1, 2, and 3.
B cannot be in the first slot, since H will need to precede it, so A cannot be correct.
D can be in the fifth slot, so answer choice B could be true.
H cannot be in the seventh slot, since B, D, and K must all come after it.
J cannot be in the sixth slot. If J was placed sixth, then B and D would have to be placed second and third, with H placed first. This would leave no legal spot for K, since J and K cannot be consecutive.
H B/D D/B F    J   
1 2 3 4 5 6 7
K cannot be in the third slot, since B, D, and H all need to precede it.


Question 4
To solve this question, begin by placing C into the third slot.
      C F/H         
1 2 3 4 5 6 7

Slots 5 and 6 are now the only legal slots for B and D to occupy, which forces K into slot 7.
      C F/H B/D D/B K
1 2 3 4 5 6 7

Now look at the answers. Since K must be assigned to slot 7, it cannot be assigned to the second slot, so E is the correct answer.


Question 5
To solve this question, begin by placing H into the first time slot. This will force F into slot 4.
  
H    F         
1 2 3 4 5 6 7


B and D can now occupy either slots 2 and 3, or else slots 5 and 6, so it is best to create two separate pictures.
  
H    F B/D D/B K
1 2 3 4 5 6 7


H B/D D/B F         
1 2 3 4 5 6 7


In the second scenario, J and K must be separated in the three remaining spots, so C must come between them.
  
H    F B/D D/B K
1 2 3 4 5 6 7


H B/D D/B F K/J C J/K
1 2 3 4 5 6 7


C can occupy either the second or third slot in the first picture, and must occupy the sixth slot in the second picture. Thus, the complete and accurate list of slots which C can occupy is second, third, and sixth, so answer choice E is correct. If you are unclear why C cannot occupy spots fifth and seventh which H is first, try creating a picture and attempting to fill it in with the other advertisements. You will not be able to separate J and K.


Question 6
To solve this question, begin by placing J into the seventh slot.
  
      F/H       J
1 2 3 4 5 6 7


H cannot occupy the fourth slot, since this would not allow enough room after it for B, D, and K. Thus F must occupy the fourth slot.
  
      F       J
1 2 3 4 5 6 7


This will leave only slots 2 and 3 open for B and D, which will force H into slot 1.
H B/D D/B F       J
1 2 3 4 5 6 7


Now K must be placed, but cannot be next to J, so it must occupy slot 5, with C leftover for slot 6.
H B/D D/B F K C J
1 2 3 4 5 6 7


Thus, K must occupy the fifth spot, which is answer choice E.





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