Three circus performers—Flo, Genie, and Kyle—will perform the following six circus acts: acrobatics; ball juggling; clowning; dunking; elephant demonstrations; fire twirling. Each act is performed only once in any given show, and only one act is performed at a time. The following conditions dictate the sequencing of these acts:

• Flo performs exactly one act before Genie performs any of her acts
• Flo does not perform first and he does not perform last
• Genie does not do acrobatics and ball juggling
• Kyle does not do acrobatics and elephant demonstrations
• Ball juggling is performed immediately after the elephant demonstrations

If Kyle performs last, then which of the following must be true?

Exactly five men—Adam, Ben, Carlos, David, and Eric—and five women—Liza, Michelle, Nicole, Olivia, and Patricia—are scheduled to take ballroom dance classes. There is one class offered each day—Monday, Tuesday, Wednesday, Thursday, and Friday—for a total of five classes. Every class has exactly one man and one woman. Every person participates in exactly one class with the following conditions:

Ben dances one day before Olivia.

Carlos and Nicole attend class on the same day.

Adam dances on Friday.

There is exactly one day between the days Ben and Carlos dance.

If Carlos dances on Monday, what must be true?

Exactly five men—Adam, Ben, Carlos, David, and Eric—and five women—Liza, Michelle, Nicole, Olivia, and Patricia—are scheduled to take ballroom dance classes. There is one class offered each day—Monday, Tuesday, Wednesday, Thursday, and Friday—for a total of five classes. Every class has exactly one man and one woman. Every person participates in exactly one class with the following conditions:

Ben dances one day before Olivia.

Carlos and Nicole attend class on the same day.

Adam dances on Friday.

There is exactly one day between the days Ben and Carlos dance.

Which is a possible and accurate order in which the women dance during the week starting with Monday?

Exactly five men—Adam, Ben, Carlos, David, and Eric—and five women—Liza, Michelle, Nicole, Olivia, and Patricia—are scheduled to take ballroom dance classes. There is one class offered each day—Monday, Tuesday, Wednesday, Thursday, and Friday—for a total of five classes. Every class has exactly one man and one woman. Every person participates in exactly one class with the following conditions:

Ben dances one day before Olivia.

Carlos and Nicole attend class on the same day.

Adam dances on Friday.

There is exactly one day between the days Ben and Carlos dance.

Which is a possible and accurate order in which the men dance during the week starting with Monday?

Exactly five men—Adam, Ben, Carlos, David, and Eric—and five women—Liza, Michelle, Nicole, Olivia, and Patricia—are scheduled to take ballroom dance classes. There is one class offered each day—Monday, Tuesday, Wednesday, Thursday, and Friday—for a total of five classes. Every class has exactly one man and one woman. Every person participates in exactly one class with the following conditions:

Ben dances one day before Olivia.

Carlos and Nicole attend class on the same day.

Adam dances on Friday.

There is exactly one day between the days Ben and Carlos dance.

If Adam and Olivia dance on the same day, what must not be true?

Exactly five men—Adam, Ben, Carlos, David, and Eric—and five women—Liza, Michelle, Nicole, Olivia, and Patricia—are scheduled to take ballroom dance classes. There is one class offered each day—Monday, Tuesday, Wednesday, Thursday, and Friday—for a total of five classes. Every class has exactly one man and one woman. Every person participates in exactly one class with the following conditions:

Ben dances one day before Olivia.

Carlos and Nicole attend class on the same day.

Adam dances on Friday.

There is exactly one day between the days Ben and Carlos dance.

Which is a possible and acceptable partial schedule for the week?

Five friends: Lenny, Monica, Nathan, Olivia, and Peter, take turns doing the following five chores: dishes, sweeping, mopping, dusting, and trash removal. Each person does exacly one chore, and each chore is done by exactly one person. To determine which friend does each chore, they apply the following rules:

• Lenny cannot sweep.
• Peter must either dust or mop.
• If Monica does dishes, then Lenny does trash removal.
• If Olivia does not do trash removal, then Peter dusts.

If Monica does dishes, which of the following must be true?

If Peter mops, all of the following are possible except:

If Inez is the only person who graduated in 2010, and Jack did not graduate the same year as Maria, which of the following could be a correct assessment of each person's graduation year?

A family is having a yard sale and pricing each type of item at $0.25, $0.50, $1.00, or $2.00. The types of items they sell are: books, CDs, dolls, flowerpots, paintbrushes, and towels.

• Flowerpots cost at least as much as dolls.
• The total price of one doll with one CD is less than the total price of one doll with one book.
• Books are the same price as paintbrushes.
• Towels cost $2.00.

If books cost $0.50 and dolls cost more than books, which of the following could be true?