I13-09

Question

The selection process for the Star Foundation Prize begins with the author registering a book, either via email or in person at the Star Foundation office. An advisory committee, comprising a writer, two publishers, and a literary agent, then shortlists 30 books. 
 
These shortlisted books are forwarded to a judging panel that includes representatives from three fields: two eminent authors, one eminent publisher, and two leading booksellers. Each panel member independently nominates one book for the prize without consulting the others. The book recommended by a majority of the judging panel is awarded the Star Foundation Prize.
 
In case the judging panel cannot reach a majority decision, the final verdict is made by the Chairman and the board of the Star Foundation, whose decision is final and binding.
 
Select for  Statement 1  and for  Statement 2  the statements such that if Statement 1 is true, then Statement 2 must be true, but it could be the case that Statement 2 is true and Statement 1 is false. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

Answer: 
 
• Statement 1: The book  Prejudice  won the Star Prize after a decision by the Chairman and the board of the Star Foundation.
 
• Statement 2: The book  Prejudice  was not nominated by members from at least one of the fields represented on the judging panel.
 
 Explanation: 
 
If Statement 1 is true ( Prejudice  won the Star Prize via the decision of the Chairman and the board), this means  Prejudice  did not secure a majority (3 or more votes) in the judging panel. Since the judging panel consists of five members representing three fields (authors, publishers, and booksellers), failing to get 3 or more votes implies that at least one representative from a field did not nominate  Prejudice . Therefore, if Statement 1 is true, Statement 2 must also be true.
 
However, Statement 2 being true ( Prejudice  was not nominated by members from at least one field) does not guarantee that  Prejudice  won via the Chairman and the board. The book could have failed to win the prize entirely.
 
 Analysis of Other Statements: 
 
• The book  Prejudice  was selected as the best read by the advisory committee.
 
We have no information about how the advisory committee selects the "best read" or how it is linked to any other event. Therefore, this statement cannot guarantee any other event (so it cannot be Statement 1) and is not guaranteed by any other event (so it cannot be Statement 2).
 
• The author of the book  Prejudice  registered it via email.
 
Registration could be done either via email or in person, so the registration method is not inherently linked to any other event in the process. This statement cannot guarantee anything (so it cannot be Statement 1) and is not guaranteed by anything else (so it cannot be Statement 2).
 
• The book  Prejudice  received more nominations from the judging panel than any other book.
 
Receiving more nominations than other books does not guarantee a majority (3 or more votes), as it could still be less than a majority, e.g., 2 votes. This means it does not necessarily lead to any other event (so it cannot be Statement 1) and is not guaranteed by any other event, as receiving more nominations does not inherently follow from any other event (so it cannot be Statement 2).

Correct answer:

Statement 1  "The book Prejudice won the Star Prize after a decision by the Chairman and the board of the Star Foundation. "

Statement 2  "The book Prejudice was not nominated by members from at least one of the fields represented on the judging panel."

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

crimson_noise · Answer

I don’t quite agree with the solution. What if?
False: The book Prejudice won the Star Prize after a decision by the Chairman and the board of the Star Foundation.
True: The book Prejudice received more nominations from the judging panel than any other book.

Bunuel · Answer

Your logic isn’t clear. Not sure what you're trying to show there. The question asks: if Statement 1 is true, then Statement 2 must be true, but Statement 2 can be true even if Statement 1 is false. How does your example fit that?

Dream009 · Answer

My answer was: Statement 1-The book Prejudice received more nominations from the judging panel than any other book.
St- 2: 
The book Prejudice was selected as the best read by the advisory committee.

Only when it received more nominations at advisory panel level - it will be selected- how is that wrong? @Bunel - please guide.

Bunuel · Answer

Your pair is not valid. The advisory committee only shortlists books, it does not choose a single “best read,” so that statement cannot be linked to anything else in the process. Also, “more nominations than other books” does not imply a majority (it could be 2 out of 5, which is still not enough to win outright).

In contrast, the official pair works: if the Chairman decided, then the judging panel did not reach a majority, which guarantees that Prejudice was not nominated by at least one of the fields. That one-way link satisfies the requirement, so the correct answer is the official one, not your pair.

Vivek1707 · Answer

This is a great question that’s helpful for learning. Very good quality question with a very subtle trap

chelsea10 · Answer

I like the solution - it’s helpful. Hi one query. Here majority means 1 or 2? as mentioned below:

1) Suppose Book A gets 2 votes and Book B,C,D get 1 votes each. Total=5 votes. So does that mean Book A has got majority votes (2 votes against 1 by others) and wins.

OR

2) Book needs 3 votes at very least out of 5 to be called majority and win ?

Question 2: If we replace "MAJORITY" with "MOST" votes then how the interpretation changes ?

Bunuel · Answer

Here, majority means more than half of the 5 votes, so a book needs at least 3 votes to get a majority.

If Book A gets 2 votes and the other books get 1 vote each, Book A has received the most votes, but it has not received a majority. In that case, the judging panel has not reached a majority decision, so the Chairman and the board would decide.

If we replaced majority with most votes, then Book A would win in your example, because 2 votes would be more than any other book received.

Isha2701 · Answer

Hi  Bunuel ,
Please help me with the second statement. I think it should not be must be true
For example.
Votes:
Author 1 → Prejudice
Author 2 → Prejudice
Publisher → Another book
Bookseller 1 → Prejudice
Bookseller 2 → Prejudice

So:
Prejudice = 4 votes
Another book = 1 vote
There is a clear majority (4 out of 5).

Therefore:
The board is never involved.
The prize is decided directly by the judging panel.

The board only steps in if there is no majority. For example:
A = 2 votes
B = 2 votes
C = 1 vote
No book has 3 or more votes, so the board decides.

If only the publisher doesn't vote for Prejudice, the other four still form a majority, so the board is not involved.

Bunuel · Answer

Your example does not satisfy Statement 1, because with 4 votes,  Prejudice  wins directly through the judging panel.

If the board made the decision, no book received a majority, so  Prejudice  received at most 2 votes. To receive nominations from all three fields, it would need at least 3 votes, one from each field. Therefore,  at least one field must have had no member nominate  Prejudice  .

I13-09

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My Rewards

Statement 1	Statement 2
		The book Prejudice was selected as the best read by the advisory committee.
		The book Prejudice won the Star Prize after a decision by the Chairman and the board of the Star Foundation.
		The author of the book Prejudice registered it via email.
		The book Prejudice was not nominated by members from at least one of the fields represented on the judging panel.
		The book Prejudice received more nominations from the judging panel than any other book.