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Critical Thinking Questions – The Thought Process Behind Answering the Questions (Part 04)

This is a continuation of Critical Thinking Questions and Evaluations - Part 03, bringing with it some new questions!

Question 10: Finance Company Manager

Question: Mr. Tory, the manager of a local finance company, was walking down his street when he found a $100 bill by the curb. He picked it up, noted the serial number, and went home. Mrs. Tory told her husband that they owed the liquor store $100, so he gave the bill to his wife to pay the liquor store. The owner of the liquor store owed the butcher $100, so he gave the bill to the butcher, who then went to a farmer and purchased a lamb with the $100. the farmer remembered he owed the finance company $100, so he took the same bill to them to pay his debt. Upon careful examination, Mr. Tory discovered that the bill was counterfeit. By this time, the $100 bill had paid $400 in debt. Which transactions turn sour and who loses what?

Thought Process

This is a pretty long question and it has a lot of details in it. As such, it is important for us to start breaking it down. First off, let us see the path of the $100 bill. This is the first step just because it appears to have importance based on the question being asked. Here we go!

  • Mr. Tory, the manager of a local finance company finds $100
  • Mr. Tory → Mrs. Tory
  • Mrs. Tory → Liquor Store ($100 in debt paid)
  • Liquor Store → Butcher ($100 in debt paid for $200 total)
  • Butcher → Farmer ($100 in debt paid for $300 total)
  • Farmer → Mr. Tory ($100 in debt paid for $400 total)

Now, with this broken down, we need to pay attention to the fact that the bill Mr. Tory found was fake. This means when he gave it to his wife it was fake, and continued down this same path all the way back to him. As a result, no debts at all were paid off. Now, there is a little bit of a trick here, though. If we look back up at the butcher's situation, he sold his lamb for $100. Being that the money was fake, he is entitled to either his $100 or his lamb back (think of it as being like giving someone a fake check for something; you either owe them the items or the money back). So while all of the others used it solely for their debt purposes, the butcher actually made a purchase with the fraudulent money.

Answer

Since the identical counterfeit bill can be traced through all of the transactions, they are all invalid. Therefore, everybody stands in relation to their respective debt as they were before Mr. Tory found the counterfeit bill. This being the case, the farmer is entitled to his lamb or $100.

Question 11: Heads Or Tails

Question: Art Conn was tossing an ordinary coin in the air and noting how many times it turned up heads. He began to think that he had a very special coin since he had tossed the coin in the air eleven times and each time it had turned up heads. Seeing Duncan Drivel across the room, Art walked over and challenged him to a small wager. Art proposed to bet one hundred to one that if he tossed the coin in the air and let it fall naturally, it would turn up heads. What is the probability that the coin will come up heads on the twelfth toss?

Thought Process

To a lot of people, this can be a tricky question. When we deal with statistics, we have to keep in mind that, under equal circumstances, the probability will remain the same regardless of any past attempts. When we are looking at this coin, it has two options: heads and tails. This means that, theoretically, if you toss it up in the air a lot of times, it should land on both of these about equal. Now, there are some things to take in to consideration here:

  • It is a probability. There are up and down swings as part of this (such as there is when you go gambling). The more repetitions you do, however, the better the chances are of you being at least close to the right mark (in this case, 50%). This could take millions of tries to get to, but regardless at some point it will happen
  • Previous attempts are irrelevant in this case. Even if it went heads a thousand times in a row (which is statistically going to happen if you do enough repetitions), the next flip is still 50% regardless

Now, a trick that this question is probably not considering is that the back and the front of coins are of different weights. Even if they were created with equality in mind, due to dirt, wear and tear, etc. they are no longer equal. As such, while we are going to go with a 50% chance (since the question does not specify otherwise), in the real world it would need to be taken in to consideration as well since it impacts the way the coin moves through the air, and would therefore also affect which side it lands on.

Answer

The odds are still 50/50. Since a coin plays no favorites and has no memory, the odds are always the same.

Question 12: Suzie's Birthday

Question: The day before yesterday Scheming Suzie was nine years old. Next year she will be twelve. How is this possible?

Thought Process

The first thought that comes to mind after reading this question is that we are dealing with leap year (being that we are skipping some years here, it appears). The problem with this is that it does not really work that way, in that each birthday would be spaced out by years, rather than having multiple birthdays in the same year. So it has to be something different.

Let us take a look at the beginning of the year (or the end of the year, depending on how you look at it). So we have December 31. What if this is her birthday?

  • December 30, 2013 – Suzie is 9
  • December 31, 2013 – Suzie turns 10
  • January 1, 2014 – This is the date of the question, so she is currently 10
  • December 31, 2014 – Suzie turns 11
  • December 31, 2015 – Suzie turns 12 (and this is also next year)

In other words, Suzie was born on December 31, and the question is being asked the day after!

Answer

The statement was made on January the first and Suzie's birthday is on December 31st. Therefore Suzie was nine the day before yesterday (December 30), she was ten yesterday (December 31), and later on this year she will be 11. therefore it stands to reason that next year she will be 12.

Trivia


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