Iggy's Logic Quiz 4

Quiz Answer Key and Fun Facts

1. You are at a carnival booth. Two boxes contain nothing, and one box contains $100. Which box should you pick if only two boxes are telling the truth? Box 1: There is nothing in Box 3 Box 2: The box the money is in is lying Box 3: Box 1 is lying

Answer: the carnival booth is rigged

If the money was in Box 1, then it is telling the truth that there is nothing in Box 3. Box 3 would then be lying, and since there are two true statements, Box 2 would have to be true. Then that would contradict the fact that Box 1 is telling the truth, so therefore the money is not in Box 1.

The money cannot be in Box 2 either since Box 2 would be self-contradictory. The money must be in Box 3. If the money is in Box 3, then Box 1 is lying, and Box 3 is truthful. Then Box 2 would have to be truthful, but then it would contradict the fact that Box 3 is telling the truth. Since everything is contradictory no matter what, the carnival booth must be rigged.

2. Which of these statements is/are true? Statement 1: Statement 4 is true Statement 2: There are at least two false statements Statement 3: Statement 4 is false Statement 4: This is the only true statement

Answer: 2 & 3

If Statement 4 was the only true statement, then all other statements are false. Statement 1 being false would contradict the fact that Statement 4 is true, therefore, Statement 4 is false.
If Statement 4 is false, then Statement 3 is true and Statement 1 is false. We already have at least two false statements, so Statement 2 is also true along with Statement 3.

3. You go to a casino table that costs $1 to play where you draw 4 cards from a normal 52-card deck. If all 4 cards you draw are kings, then you win $7,311,615. Is the prize amount fair?

Answer: The prize amount benefits you

Determining whether the prize amount is fair, is based on what the odds of winning are. The odds of drawing just one king, is 4/52, or a 1 in 13 chance. The odds of drawing another king would be 3/51, or a 1 in 17 chance. So the odds of drawing two kings are 1/13 * 1/17, or a 1 in 221 chance.

The odds of drawing a third king would be 2/50, or a 1 in 25 chance. Multiply that by a 1 in 221 chance and you get a 1 in 5525 chance of drawing three kings. The odds of drawing the last king are 1 in 49, so multiply that by 1 in 5525 and the final probably of drawing four kings is 1 in 270725. Since the casino costs $1 per play, a prize that would be equally fair, is $270,725. Since the prize is much higher than that, the prize amount benefits you.

4. A fugitive has escaped from prison and flees to an intersection where he has the choice of three alleys to hide in. He quickly chooses an alley at random and hides. An officer chasing him chooses an alley at random and plans to search. The fugitive's friend gives the police an anonymous tip that the fugitive is hiding in an alley other than the one the officer wants to search, and other than the one the fugitive is really hiding in. The officer searches the alley the anonymous caller told him to search, and finds it empty. The fugitive's friend realizes the trouble he's in, so he admits his trick to the police. The friend then runs away before revealing where the fugitive is really hiding. The officer can now search the alley he was originally going to search, search the alley he already searched, or search the remaining alley. What should the officer do?

Answer: Search the remaining alley

I'll use a list of the possible scenarios:

"empty"-fugitive-empty
"empty"-empty-fugitive
"fugitive"-empty-empty

The quotation marks represent the alley the officer was going to search. When the officer searches the wrong alley, one of the empty alleys goes away, leaving the possible scenarios:
"empty"-fugitive
"empty"-fugitive
"fugitive"-empty
The officer's original choice of alley is only correct 1 in 3 times. It is more logical based on probability to search the remaining alley since the fugitive is hiding there 2 in 3 times.

5. Four people are found in an alley after reported fighting. Two people are victims, while the other two are the attackers. The attackers are lying, and the victims are telling the truth. Based on that information, who were the two attackers? TJ: Drake beat me up Jake: I saw RJ getting attacked Drake: TJ beat me up RJ: I saw Jake getting attacked

Answer: TJ and Drake

Since TJ and Drake are accusing each other, then one or both of them is an attacker. If Jake was an attacker, then he's lying that RJ was attacked, which means RJ is also an attacker. That's impossible since there would be more than two attackers. Jake must be telling the truth. Since Jake is truthful, then RJ is also truthful and innocent, which only leaves TJ and Drake as attackers.

6. Four people are possible suspects in robbing a bank. Two of the people worked together to rob the bank, while the other two are innocent. The guilty people are lying, while the innocent people are telling the truth. Who were the robbers? Connor: Reese was one of the robbers Emma: Bud was one of the robbers Bud: Connor and Emma were the robbers Reese: Emma was not one of the robbers

Answer: Bud and Connor

If Bud is telling the truth that Connor and Emma were the robbers, then Reese would be innocent, and therefore telling the truth that Emma was not one of the robbers, which would contradict the fact that Connor and Emma were the robbers. This means Bud is lying, and he is one of the robbers. If Emma was the other robber, then Reese would be lying, resulting in three robbers. So Emma is not the other robber, and Reese is telling the truth.

This means Connor has to be the other robber, so Bud and Connor robbed the bank.

7. It takes Ray 3 hours to clean the house. It takes Craig 2 hours to clean the house. How long would it take for them to clean it together?

Answer: 72 minutes

Let's say the house is 6 units of dirtiness. Ray would clean 2 units per hour, and Craig would clean 3 units per hour. Together they would clean 5 units per hour, so it would take them 6/5 of an hour to clean the house, which is 72 minutes.

8. A man escapes from jail with help from his girlfriend. Four girls are accused of being the man's girlfriend. His girlfriend is lying. Two girls are innocent and telling the truth. The other girl is the man's sister who is helping the girlfriend lie. Who is the man's sister? Amanda: Melinda is his girlfriend Vanessa: Eva is lying Eva: Amanda is lying Melinda: Vanessa is not his sister

Answer: Amanda

If Amanda is telling the truth, then Melinda is lying. If Melinda is lying, then Vanessa is his sister. If Vanessa is his sister, then she's lying about Eva lying. If Eva isn't lying, then Amanda is lying, which would contradict the fact that Amanda's telling the truth. That means Amanda is lying and could be his girlfriend or sister. Eva must be telling the truth since Amanda has to be lying. So Vanessa must also be lying, and Melinda is telling the truth. Since Melinda's telling the truth, Vanessa isn't his sister and must be his girlfriend. Amanda is the other liar, so she must be his sister.

9. Which of these has the greatest probability of happening if you roll two dice?

Answer: rolling two even numbers

The odds of rolling an even number are 1 in 2, and the odds of rolling another are 1 in 2. So the odds of rolling two even numbers are 1 in 4.
1-6, 6-1, 2-5, 5-2, 3-4, 4-3, are the possible combinations of the dice adding up to 7. There are 36 possible dice rolls, so a 1 in 6 chance of rolling a 7.
The only multiples of 6 that can be rolled are 6 and 12. The possible combinations are 1-5, 5-1, 2-4, 4-2, 3-3, and 6-6. So the odds are 6 in 36, or 1 in 6.
The odds of rolling two of the same number are 1 in 6 because the odds of rolling a number are 1 in 1, and the odds of rolling the same number are 1 in 6.
The odds of rolling two even numbers is 1 in 4, which is more than all the other odds, which are all 1 in 6.

10. Haley, Octavio, Ray, and Kate are found in an alley at midnight and accused of robbing a house. If only the two thieves' statements are false, then who were the thieves? Kate: It was Haley and Octavio Haley: It was Kate and Ray Octavio: It was Kate and I Ray: It wasn't me

Answer: Octavio and Haley

Octavio cannot be telling the truth since he is incriminating himself. Octavio must be lying, and Kate cannot be his partner. Since Kate is telling the truth, Haley and Octavio were the thieves.

Source: Author iggy4

This quiz was reviewed by FunTrivia editor crisw before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.

This quiz is mostly logic and common sense, although you do need legitimate math knowledge for some of the questions.

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