Question

Fact 1: A town is hosting a 3-day music festival, which will feature a rock band show by local artists for the very first time.
Fact 2: 2000 tickets have been sold for the show.
Fact 3: The ticket sale will end next Monday.
Fact 4: The organizing committee has been working for the past 10 weeks to organize this event.
If the above statements are facts, which of the statements below must also be facts?
I. A few hundred seats will remain empty during the festival.
II. The family members of the rock band performers will be present at the festival.
III. Since the preparation started 10 weeks ago, all tickets will be sold by Monday.

• A. Only I
• B. Only III
• C. Only I and II
• D. Only II and III
• E. None of them

Hint:

For must-be-true questions, try to imagine a valid alternative scenario that fits every given fact but still makes the statement false; if even one such scenario is possible, that statement is not guaranteed and should be rejected.

Answer 1

Answer: (E)

Step 1: Understand the nature of a “must be true” question.
A statement must be true only if it logically and necessarily follows from the given facts, without adding assumptions.
Step 2: Analyze Statement I.
There is no information about the total seating capacity of the festival. Hence, we cannot conclude that any seats will remain empty. This statement does not necessarily follow.
Step 3: Analyze Statement II.
There is no mention of the performers’ family members in the given facts. Their presence at the festival cannot be inferred. Hence, this statement is not necessarily true.
Step 4: Analyze Statement III.
Although ticket sales have been ongoing and preparation started 10 weeks ago, there is no guarantee that all tickets will be sold by Monday. This is an assumption, not a fact.
Step 5: Final conclusion.
None of the given statements must necessarily be true based on the provided facts alone.
Final Answer:
\[ \boxed{\text{Option (E)}} \]

Answer 2

Concept:

• A statement is guaranteed to be true only if every scenario consistent with the given facts also makes that statement true.
• Test each statement using a counter-example check: try to build one valid scenario that fits all the given facts but still makes the statement false. If such a scenario exists, the statement is not guaranteed.

Step 1: List exactly what the four facts guarantee.
A 3-day festival, a first-time local rock band show, 2000 tickets sold, sale ending next Monday, and 10 weeks of preparation. Nothing here states the venue capacity, the presence of relatives of the performers, or the final tally of tickets sold.

Step 2: Test Statement I, that a few hundred seats will remain empty.
This depends entirely on venue capacity, which is never given. A venue built for exactly 2000 people, or fewer, is fully consistent with the facts and would leave no seats empty, so I is not guaranteed.

Step 3: Test Statement II, that family members of the performers will attend.
Family attendance is never mentioned or implied by any fact. A scenario where not a single relative attends is entirely consistent with the four facts, so II is not guaranteed.

Step 4: Test Statement III, that all tickets will sell out because preparation began 10 weeks earlier.
Preparation time has no logical bearing on ticket demand. A well-organised event can still have unsold tickets on the closing day, and this does not contradict any of the four facts, so III is not guaranteed either.

Step 5: Combine the results.
Since a valid counter-scenario exists for each of I, II, and III individually, none of them follows necessarily from the given facts.

Final Answer: None of them