Two siblings, P and Q, worked together to steal cookies from their par

Question

Two siblings, P and Q, worked together to steal cookies from their parents' cookie jar. After their parents discovered this behavior, P and Q were taken to separate rooms and offered the following choices: to confess about the other sibling's involvement in the incident or to refuse to confess about that sibling's involvement. If both P and Q refuse to confess, they both do not get to play with their favorite toy for one day. If they each confess, they both do not get to play with their favorite toy for three days. If only one of them confesses, while the other refuses to confess, the one who confessed may play with the favorite toy right away, and the one who refused to confess does not get to play with the favorite toy for seven days. Both P and Q want only to maximize their own play time with their favorite toy.

Based only on information in the passage above, select (1) the most logical action for P to take if P hears Q confessing and (2) the action that, if Q discovered P were intending to take it, would lead Q to refuse to confess. Make only two selections, one in each column.

Sajjad1994 · Accepted Answer

Official Explanation

Analyze the information

You must complete the two scenarios logically based on the information in the passage. P and Q each have only two choices: to tell or not to tell on the sibling (they are not asked about their own involvement, and if they volunteer such information, it has no consequences). In terms of getting to play with the favorite toy as soon as possible, the best scenario involves telling on the other sibling when the other doesn't tattle (play right away), the second-best involves not telling when the other sibling also doesn't tell (lose play privileges for 1 day), the third-best involves tattling when the other also tells (lose play privileges for 3 days), and the worst involves not telling on the other when the other tattles (lose play privileges for 7 days). Keep these conditions and consequences in mind as you consider the choices.

Approach strategically

The first part of the scenario provides a condition and asks for a consequence: if P hears Q confessing, then P should ___. When Q confesses, P should also confess. While P will lose some play time with her favorite toy, she will lose even more play time if she refuses to confess.

The second part of the sentence provides a consequence and asks for a condition that triggers that consequence: if Q discovers that P will ___, then Q should refuse to confess. Such refusal works to Q's benefit the most when P also refuses to confess: each sibling loses only one day of play time with their favorite toy. (If Q found out that P was going to confess, then Q should confess.)

For the record, the passage does not discuss any consequences of confessing or refusing to confess one's own stealing behavior, so "Confess that both P and Q stole" is incorrect for both columns. For the same reason, "Confess only that P stole" and "Refuse to confess that P stole" are incorrect for both columns.

The correct answers are these:

(1): Confess only that Q stole
(2): Refuse to confess that Q stole

TAKEAWAY:  When determining what conditions or consequences must hold in a particular scenario, be careful not to go beyond the given information. Jotting down that information can help organize it and deal with it logically.

Apt0810 · Answer

1)If P hears Q confessing the he should also confess that Q stole the cookies because if Doesn't confess than P would be losing the toy for seven days
2)If P comes to know that Q refuses to confess, than P should also refuses to confess that Q stole the cookies so that both will loss the toy for 1 day

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ConfusedSEA · Answer

Apt0810  logically answered the correct answer. However, based on the answer choices provided, that will be wrong

There is no mention of confessing or refusing to confess one's own stealing from the passage. Hence the below are incorrect for both columns:
- "Confess that both P and Q stole" 
- "Confess only that P stole"
- "Refuse to confess that P stole"

Between the remaining "Confess only that Q stole" & "Refuse to confess that Q stole"
The correct answers are these:
(1): Confess only that Q stole
(2): Refuse to confess that Q stole

harrypotter14 · Answer

Sorry to revive this topic... but I'm quite confused in the solution to part (2)

"select ... the action that, if Q discovered P were intending to take it, would lead Q to refuse to confess"

Everyone above says the answer is "Refuse to confess that Q stole"

That would mean the following statement is true:

If Q discovered that P were intending to  , then Q would refuse to confess

But if Q knows that P is going to refuse to confess, then Q's options are:
1) Refuse to confess -> Both P & Q refuse leads to both losing toy for 1 day
2) Confess -> Q Confesses, P refuses leads to Q getting toy immediately and P losing toy for 7 days

Since the problem specifies that "Both P and Q want only to maximize their own play time with their favorite toy," that means Q doesn't mind that P loses their toy for 7 days. Q only cares about minimizing their own punishment.  So if P refuses to confess, wouldn't Q's best path be to confess to get the toy immediately ?

What am I missing in the above solution?

Similarly, if Q knows that P is going to confess, then Q's options are:
1) Refuse to confess -> Q loses toy for 7 days, P gets toy immediately
2) Confess -> Both confess, Q & P both lose toy for 3 days

In this situation, Q's best path is still to Confess, to minimize the number of days without their toy (3 days instead of 7 days)

I'm stuck, because in both cases it seems like Q's best path is always to Confess, but the problem asks for when will Q decide their best path is to refuse to confess

(1)	(2)
		Confess only that Q stole the cookies
		Refuse to confess that P stole the cookies
		Confess that both P and Q stole the cookies
		Refuse to confess that Q stole the cookies
		Confess only that P stole the cookies

Two siblings, P and Q, worked together to steal cookies from their par

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Two siblings, P and Q, worked together to steal cookies from their par

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