A storage facility for race cars has six garages, positioned side-by-side and numbered sequentially, from left to right, 1 through 6. Each garage stores a specific car and only that car. The cars have names given to them by their owners: Fury, Grand Slam, Lambast, Moxie, Piston, and Titrus.

The following conditions apply:

The garage storing Grand Slam is numbered higher than the garage holding Lambast.

The garage storing Lambast is numbered higher than the garage storing Titrus.

Piston is stored somewhere to the right of where Fury is stored.

Titrus is stored next to Piston.

Which one of the following must be false?

A storage facility for race cars has six garages, positioned side-by-side and numbered sequentially, from left to right, 1 through 6. Each garage stores a specific car and only that car. The cars have names given to them by their owners: Fury, Grand Slam, Lambast, Moxie, Piston, and Titrus.

The following conditions apply:

The garage storing Grand Slam is numbered higher than the garage holding Lambast.

The garage storing Lambast is numbered higher than the garage storing Titrus.

Piston is stored somewhere to the right of where Fury is stored.

Titrus is stored next to Piston.

Which one of the following could be the garage storing Lambast?

A tour guide will bring a group of tourists to seven sites—the sites are designated as A, B, C, D, E, F, and G. The tour will span the course of three days, Friday, Saturday, and Sunday. The first two sites will be visited on Friday. The next three sites will be visited on Saturday. The final two sites will be visited on Sunday.

The tour guide will organize the site visits according to the following rules:

Site A must be visited on Sunday.

Since site B is closed on Friday, it cannot be visited on that day.

Site C must be visited after site B is visited and before site D is visited.

Which one of the following could be the order in which the tour guide organizes the site visits?

A tour guide will bring a group of tourists to seven sites—the sites are designated as A, B, C, D, E, F, and G. The tour will span the course of three days, Friday, Saturday, and Sunday. The first two sites will be visited on Friday. The next three sites will be visited on Saturday. The final two sites will be visited on Sunday.

The tour guide will organize the site visits according to the following rules:

Site A must be visited on Sunday.

Since site B is closed on Friday, it cannot be visited on that day.

Site C must be visited after site B is visited and before site D is visited.

Which one of the following pair of site visits is the tour guide precluded from adopting, in either order?

A boy band (composed of Henry, Ralph, and Viktor) will play one song a day in a six-day music festival from Sunday to Friday. They have 10 total songs and will play a different song each day.  Two songs will be chosen from among the three songs written by Henry – 1, 2, and 3: two from among the four songs written by Ralph – 4, 5, 6, and 7; and two from the songs written by Viktor – 8, 9, and 10.  The following rules also apply:

1.   If song 5 is selected, then song 2 is also selected.
2.   If song 4 is selected, then neither songs 2 nor 6 can be selected.
3.   If song 8 is selected, then neither songs 10 nor 7 can be selected.
4.   If both songs 2 and 6 are selected, then song 2 is played at some time before song 6.
5.   Song 8 cannot be played on Thursday unless one of Ralph’s songs is played on Sunday. 

If 2, 6, and 9 are the first three songs to be played, not necessarily in the order given, which one song CANNOT be played on Thursday?

Three basketball players: Penny, Xerxes, and Lee, participate in a slam dunk showcase where six total dunks are executed collectively by the players.  The following rules apply:

1.   Xerxes executes exactly two dunks, at least one of which must be the first or the second dunk.

2.   Penny executes exactly three dunks, but none consecutively

3.   Lee does not execute a dunk immediately prior to or after Xerxes executes a dunk.

Which of the following cannot be true?

Three basketball players: Penny, Xerxes, and Lee, participate in a slam dunk showcase where six total dunks are executed collectively by the players.  The following rules apply:

1.   Xerxes executes exactly two dunks, at least one of which must be the first or the second dunk.
2.   Penny executes exactly three dunks, but none consecutively
3.   Lee does not execute a dunk immediately prior to or after Xerxes executes a dunk.

Which of the following could be an acceptable order, from first to sixth, of the players dunking in the showcase?

Madeline, Natalie, Rachel, Stacey, Ursula, and Valerie are six kindergarten students on a picnic with their teacher. The teacher is seated in the center with the children seated on six separate cushions arranged in a clock-wise circular fashion around their teacher.  The cushions are numbered 1 through 6 with cushion 1 at the 12 o’clock position, cushion 2 at the 2 o’clock position, cushion 3 at the 4 o’clock position, cushion 4 is at the 6 o’clock position, cushion 5 at the 8 o’clock position, and cushion 6 at the 10 o’clock position.  The following rules apply:

1.   “Adjacent” cushions are those cushions that are consecutively numbered. Cushions 1 and 6 are also considered adjacent.

2.   Stacey and Rachel are not sitting in adjacent cushions

3.   Natalie is sitting in cushion 1 or cushion 4

4.   Ursula and Stacey are sitting in adjacent cushions on either the left of right side of the clock-wise circle (i.e. cushions 2 and 3, or cushions  5 and 6)

If Valerie is sitting in cushion 4, then which of the following pairs must be sitting in adjacent seats?

Madeline, Natalie, Rachel, Stacey, Ursula, and Valerie are six kindergarten students on a picnic with their teacher. The teacher is seated in the center with the children seated on six separate cushions arranged in a clock-wise circular fashion around their teacher.  The cushions are numbered 1 through 6 with cushion 1 at the 12 o’clock position, cushion 2 at the 2 o’clock position, cushion 3 at the 4 o’clock position, cushion 4 is at the 6 o’clock position, cushion 5 at the 8 o’clock position, and cushion 6 at the 10 o’clock position.  The following rules apply:

1.   “Adjacent” cushions are those cushions that are consecutively numbered. Cushions 1 and 6 are also considered adjacent.
2.   Stacey and Rachel are not sitting in adjacent cushions
3.   Natalie is sitting in cushion 1 or cushion 4
4.   Ursula and Stacey are sitting in adjacent cushions on either the left of right side of the clock-wise circle (i.e. cushions 2 and 3, or cushions  5 and 6)

The seating arrangement of the six children could be which of the following?

Madeline, Natalie, Rachel, Stacey, Ursula, and Valerie are six kindergarten students on a picnic with their teacher.  The teacher is seated in the center with the children seated on six separate cushions arranged in a clock-wise circular fashion around their teacher.  The cushions are numbered 1 through 6 with cushion 1 at the 12 o’clock position, cushion 2 at the 2 o’clock position, cushion 3 at the 4 o’clock position, cushion 4 is at the 6 o’clock position, cushion 5 at the 8 o’clock position, and cushion 6 at the 10 o’clock position. The following rules apply:

1. “Adjacent” cushions are those cushions that are consecutively numbered.  Cushions 1 and 6 are also considered adjacent.

2. Stacey and Rachel are not sitting in adjacent cushions

3. Natalie is sitting in cushion 1 or cushion 4

4. Ursula and Stacey are sitting in adjacent cushions on either the left of right side of the clock-wise circle (i.e. cushions 2 and 3, or cushions  5 and 6)

If Rachel is sitting in cushion 1, then which child must be sitting adjacent to her?