# LSAT Logic Games : Solving four- and five-variable logic games

## Example Questions

### Example Question #41 : Four & Five Variable

There are five scientists in a laboratory: Abbi, Barry, Carri, Danny, and Evi. Each scientist performs experiments with one of three pieces of equipment: the laser, the test tube, or the microscope. The following conditions must apply:

• Abbi and Barry do not use the same piece of equipment as each other, nor do they use the same piece of equipment as Danny.
• Exactly two scientists use the laser.
• Evi and Danny use different pieces of equipment.
• If either Abbi or Carri use the microscope, they both use the microscope.

If Abbi uses the laser, which of the following are all the scientists who could use the microscope?

Danny, Evi, Carri

Barry, Danny, Evi

Barry

Danny, Carri

Barry, Evi

Barry, Danny, Evi

Explanation:

If Abbi is on the laser, that leaves four scientists to use the microscope. The only condition which would preclude any of them from possibly using the microscope is that if Carri is on the microscope, then so also must Abbi, which Abbi cannot because Abbi is on the laser. That leaves Barry, Danny, and Evi to possibly use the microscope.

### Example Question #42 : Solving Four And Five Variable Logic Games

There are five scientists in a laboratory: Abbi, Barry, Carri, Danny, and Evi. Each scientist performs experiments with one of three pieces of equipment: the laser, the test tube, or the microscope. The following conditions must apply:

• Abbi and Barry do not use the same piece of equipment as each other, nor do they use the same piece of equipment as Danny.
• Exactly two scientists use the laser.
• Evi and Danny use different pieces of equipment.
• If either Abbi or Carri use the microscope, they both use the microscope.

If the condition that exactly two scientists use the laser is changed to exactly three scientists must use the laser. Which of the scientists must now either use the microscope or the test tube?

Barry

Abbi

Evi

Carri

Danny

Danny

Explanation:

Since there are five scientists and Abbi, Barry, and Danny must be using different pieces of equipment, that means both Carri and Evi must use the laser in addition to Abbi, Barry or Danny. Because Danny cannot use the same equipment as Evi, that precludes Danny from using the laser. There being no such restrictions on Abbi or Barry, Danny is the correct answer.

### Example Question #41 : Four & Five Variable

A quarterback has time left in the game to call exactly seven plays—L, M, N, O, P, S, and T—one at a time and in any order according to the following conditions:

• Play P is called either first or last.
• The quarterback calls L at some point before calling N.
• The quarterback calls M at some point before calling T.
• The quarterback calls exactly one play between calling play L and play O.
• The quarterback calls exactly one play between calling play M and play P.

Which of the following lists is the order the quarterback could call the plays from first to last?

L, N, S, O, M, T, P

M, T, P, S, L, N, O

P, N, M, S, O, T, L

P, T, M, S, L, N, O

O, S, L, N, M, T, P

O, S, L, N, M, T, P

Explanation:

Using the process of elimination, go through the conditions one by one. Four of the possible answers violate one or more of the conditions. O, S, L, N, M, T, P is the only sequence that does not violate any of the conditions.

### Example Question #41 : Solving Four And Five Variable Logic Games

A quarterback has time left in the game to call exactly seven plays—L, M, N, O, P, S, and T—one at a time and in any order according to the following conditions:

• Play P is called either first or last.
• The quarterback calls L at some point before calling N.
• The quarterback calls M at some point before calling T.
• The quarterback calls exactly one play between calling play L and play O.
• The quarterback calls exactly one play between calling play M and play P.

Which one of the following could be true?

T is called first

N is called first

M is called fourth

S is called last

T is called second

S is called last

Explanation:

Because of the condition where M must be called one placeholder away from P, M must be either third or fifth. Because of the placement of M, T cannot be placed before placeholder four. N must be called after L and so cannot be called first because L would then have to go in placeholder zero, which does not exist. Using the process of elimination, that leaves "S is called last" as the correct answer.

### Example Question #43 : Four & Five Variable

A quarterback has time left in the game to call exactly seven plays—L, M, N, O, P, S, and T—one at a time and in any order according to the following conditions:

• Play P is called either first or last.
• The quarterback calls L at some point before calling N.
• The quarterback calls M at some point before calling T.
• The quarterback calls exactly one play between calling play L and play O.
• The quarterback calls exactly one play between calling play M and play P.

If T is called fourth, what play must the quarterback call last?

P

L

S

O

N

O

Explanation:

If T is called fourth, then M must be called third, and P called first. If you consider that the L and O must be placed one placeholder apart and the only place left to do that is placeholders five and seven, then we can know that either L or O must be placed last. L must be placed before N so therefore five, six and seven are L, N, O respectively.

### Example Question #44 : Four & Five Variable

A quarterback has time left in the game to call exactly seven plays—L, M, N, O, P, S, and T—one at a time and in any order according to the following conditions:

• Play P is called either first or last.
• The quarterback calls L at some point before calling N.
• The quarterback calls M at some point before calling T.
• The quarterback calls exactly one play between calling play L and play O.
• The quarterback calls exactly one play between calling play M and play P.

If the quarterback calls play M at some time after calling play O, the fifth play called could NOT be which one of the following?

T

N

S

M

L

L

Explanation:

The fifth play cannot be L because then the third play must be O. The last play cannot be O because both M and T come after O. If the third play is O and the fifth is L, then there is no placeholder for M because M must come with one placeholder between it and P. All the spaces that could fulfill that requirement would already be filled.

### Example Question #45 : Four & Five Variable

Five dogs are finalists in a dog-show competition:  Fifi, Glee, Haley, Jo, and Kay.  They will appear on a platform singly and only once during the final phase of the competition.  The order of their appearance must accord with the following rules:

Glee must appear earlier than Fifi.

Kay must appear earlier than Haley and Jo.

Haley must appear either immediately before or immediately after Fifi.

Which one of the following could be the order, from first to last, in which the dogs appear on the platform?

Kay, Glee, Jo, Fifi, Haley.

Glee, Fifi, Haley, Kay, Jo

Glee Jo, Kay, Haley, Fifi

Glee, Kay, Haley, Jo, Fifi

Kay, Jo, Fifi, Haley, Glee

Kay, Glee, Jo, Fifi, Haley.

Explanation:

For acceptability questions like this one, apply each rule to the answer choices and find the rule-violators.  The one answer that is not eliminated is, by definition, a non-violator and thus the correct answer.

### Example Question #41 : Solving Four And Five Variable Logic Games

Five dogs are finalists in a dog-show competition:  Fifi, Glee, Haley, Jo, and Kay.  They will appear on a platform singly and only once during the final phase of the competition.  The order of their appearance must accord with the following rules:

Glee must appear earlier than Fifi.

Kay must appear earlier than Haley and Jo.

Haley must appear either immediately before or immediately after Fifi.

All of the following can be true, EXCEPT

Kay appears immediately before Fifi.

Kay appears immediately before Haley.

Kay appears immediately after Fifi.

Jo appears immediately before Glee.

Jo appears immediately before Fifi.

Kay appears immediately after Fifi.

Explanation:

This question can be answered efficiently by consulting the sequencing rules (arrived at through making deductions):

G --- F/H either order

K --- F/H

K --- J

Among the answer choices, the one that cannot happen is the appearance of K immediately after F.

### Example Question #43 : Solving Four And Five Variable Logic Games

Five dogs are finalists in a dog-show competition:  Fifi, Glee, Haley, Jo, and Kay.  They will appear on a platform singly and only once during the final phase of the competition.  The order of their appearance must accord with the following rules:

Glee must appear earlier than Fifi.

Kay must appear earlier than Haley and Jo.

Haley must appear either immediately before or immediately after Fifi.

The order in which the dogs appear on the platform is fully determined if which one of the following is true?

Fifi appears immediately before Haley.

Jo appears immediately before Haley.

Kay appears immediately before Fifi.

Glee appears immediately before Fifi.

Haley appears immediately before Jo.

Kay appears immediately before Fifi.

Explanation:

If K appears immediately before F, then we know that there must be a KFH block.  We also know that J must appear after K, so the block is extended:  KFHJ.  We know that G must be before the KFH block, so the block is further extended:  GKFHJ.  Thus, the answer is that the sequence is fully determined if we know that K appears immediately before F.

### Example Question #42 : Solving Four And Five Variable Logic Games

Five dogs are finalists in a dog-show competition:  Fifi, Glee, Haley, Jo, and Kay.  They will appear on a platform singly and only once during the final phase of the competition.  The order of their appearance must accord with the following rules:

Glee must appear earlier than Fifi.

Kay must appear earlier than Haley and Jo.

Haley must appear either immediately before or immediately after Fifi.

Of the final five finalists, how many of the dogs could appear on the platform fourth?

four

three

one

two

five

two

Explanation:

Consult the sequence:

G --- F/H

K --- F/H

K --- J

Fourth is the second to last slot.  Clearly, G and K cannot appear in that slot.  So that leaves F, H, and J.  But F and H must be next to each other, so J cannot appear in the fourth slot, as that would force a separation between F and H.  Accordingly, only two dogs could be in that fourth slot, F or H.