Question

A dance academy instructor must schedule eight dance classes--a charleston class, a foxtrot class, a jitterbug class, a limbo class, a polka class, a rumba class, a tango class, and a waltz class--for a single day. Exactly two classes will be scheduled at a time, and the scheduling must be made according to the following conditions:

The limbo class and the rumba class are not scheduled for the same time.
The charleston class and the polka class must be scheduled for the same time.
The limbo class is scheduled at some time after the polka class.
The rumba class and the waltz class are not scheduled for the same time.

If the tango class is scheduled for the same time as the foxtrot class, which one of the following must be true?
(A) The jitterbug class and the limbo class must be scheduled for the same time.
(B) The jitterbug class and the rumba class must be scheduled for the same time.
(C) The jitterbug class and the waltz class must be scheduled for the same time.
(D) The limbo class and the rumba class must be scheduled for the same time.
(E) The rumba class and the waltz class must be scheduled for the same time.

Answer 1

When the tango class is scheduled with the foxtrot class, the mandatory pairing that must emerge, considering all conditions, is that the jitterbug class and the waltz class must be scheduled for the same time.

Step-by-step explanation:

If the tango class is scheduled for the same time as the foxtrot class, we are trying to determine which pairing must be true as a consequence. From the conditions given, we know the following:

• The limbo class cannot be scheduled at the same time as the rumba class.
• The charleston class and the polka class must be scheduled for the same time.
• The limbo class is scheduled at some time after the polka class.
• The rumba class and the waltz class are not scheduled for the same time.

We have four pairs of classes to schedule concurrently. If tango and foxtrot are paired together, this leaves six classes to be paired off. Given that charleston and polka are paired, that leaves limbo, jitterbug, rumba, and waltz. Since limbo cannot be with rumba and must be after polka, and rumba cannot be with waltz, it leaves the only possible pairing to be jitterbug with waltz. Therefore, choice (C) The jitterbug class and the waltz class must be scheduled for the same time must be true.