Real World Graduation, Question 83: Rat Sightings

RealWorldGraduation_Question_83_Rat_Sightings   <– PDF

There are 8.143 million (8,143,000) people and an estimated 25 million (25,000,000) rats in the New York City metropolitan area.  Suppose that the estimated rat population is accurate.  The area of the metropolitan area is 322 square miles (8,976,844,800 square feet).  Therefore, density of rats is 25,000,000/8,976,844,800 = .002784 rats per square foot, or one rat for every 359 square feet.    Likewise, the density of people is 8,143,000/8,976,844,000 = .000907 persons per square foot, or one person per 1102.4 square feet.  Since the density of rats is higher, and an area of 359 sq. ft. is a square with sides 18.9 ft long, and since the distance from the center of such a square to any corner (where a person could be) is 26.8 ft, a researcher has concluded (to a first approximation) that a person in New York City is at most (on average) 26.8 ft. from a rat.

On the other hand, another researcher conducted a survey about how often rats are observed in New York City.  Some people reported seeing rats every day, while others could not recall the last time they saw one, even for protracted periods.   A survey was taken in 2002.  In the survey, people were asked if they had seen rats or evidence of rats in their homes in the previous 90 days.  On the upper end, 43% of Hispanic people with income less than $25,000 had seen rats or evidence of them, while only 10% of white people making over $50,000 saw them [1].  Other income levels among whites and Hispanics fell between these two extremes, as did the data for black people of all income levels.

How can these two sets of facts about rats be reconciled?

a) They can be reconciled if one recalls that white people and some upper-class black people have high rates of baseball bat ownership, which rats fear the most.

b) They can be reconciled if one realizes that some people in New York live in expensive neighborhoods and others live in slums because they are victims of the rich. Since rats prefer to live in the poorer neighborhoods because the rodent controls are not as effective, it is logical that some (the poor) see rats every day while others (the rich) never see them.

c) They can be reconciled if one recalls that averages do not apply here because rats prefer to live near people of Hispanic descent because Hispanics throw out a lot of unused vegetables, which are the favorite food of rats.

d) The data can be reconciled because most blacks and nearly all whites will deny or minimize any rat problems in their homes.

e) The data can be reconciled because most Hispanics will exaggerate any rat problems in their homes.

[1]   A. Karpati, B. Kerker, F. Mostashari, T. Singh, A. Hajat, L. Thorpe, M. Bassett, K, Henning, T. Frieden, Health Disparities in New York City, NY: New York City Department of Health and Mental Hygiene, 2004, p. 23


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Real World Graduation, Question 82: Pennies

RealWorldGraduation_Question_82_Pennies   <– PDF

There has been some discussion in recent years about the utility of small-denomination U. S. coins such as the penny and the nickel.  Some people have concluded that we would be better off to abolish these coins.  What is the most plausible reason for abolishing the penny?

a) The buying power of the penny is so low as to not be worth continuing; for example, there is no such thing as “penny candy” any more.

b) The penny is too heavy to justify carrying around, when considered with regard to its buying power.

c) The effect of monetary inflation has made penny nearly worthless. People don’t even collect change if it is only a few cents; people won’t stop to pick up a penny on the street.

d) It has always been an inconvenience, since it is nearly the same size as a dime.

e) Some combination of a), b), and c).

(The answer is on p. 2 of the PDF.)

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Real World Graduation, Question 81: Test Drives

RealWorldGraduation_Question_81_Test_Drives   <– PDF

A person went to a new car dealer to buy a new car. He found one that he was interested in, and the dealer offered to let him take a test drive, but required that the prospective buyer first provide his drivers license so the dealer could make a copy of it before the test drive.  Why did the dealer want to see the license and make a copy?

a) To check with the police to see if the prospective buyer has any outstanding arrest warrants and report him to the local police.

b) To make sure the prospective buyer is legally allowed to buy a car.

c) To see if the prospective buyer has any unpaid parking tickets, and report him to the local parking violation bureau.

d) To verify that the prospective buyer has adequate automobile insurance, in case of an accident during the test drive.

e) Some combination of the above, which varies from state to state depending on the state and local laws.

(The answer is on p. 2 of the PDF.)

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Real World Graduation, Question 80: Encryption

RealWorldGraduation_Question_80_Encryption   <– PDF

A certain foreign group is in the business of smuggling heroin into the U. S. They are aware that the FBI and DEA have tapped their phones and are monitoring their emails.  They wish to communicate to their allies in the U. S. that: a) a shipment of 40 kg of heroin is available; b) it will brought into New Orleans, LA on the 14th of April; and c) they will meet their co-conspirators at the pre-arranged safe-house at noon.  It is decided to send this message by posting it on a blog using a pre-arranged user name, and using an encryption method developed by the group and their allies.  Thus, even though the blog were being monitored by the FBI and the DEA, they believe a sufficiently strong code will prevent the police from figuring out what is going on.

Here are the candidate codes they have developed, each of which sends the message above:


2)         B9X42 N83 FGJPT 6HOGD 9JNU 49 BPO954E VB6 R5 4E3F GA 78HB

3)         83927 83261 90943 74835 12772 81934 61732 91846 91034 17283 81926 88225

4)         #7(*^ %^#ED *(K 7H 9JH6& FGR^N GHE$4 GH*DE H&%%B &()UH ERBVG


Which is the most effective way for the drug dealers to send their secret message?

a) Code #1, because it is the shortest, and hence the most efficient.

b) Code #2, because it uses numbers and letters and has no repeating sequences.

c) Code #3, because it consists only of numbers in a uniform sequence of 5 characters, which does not give any hint about what words are being represented.

d) Code #4, because it uses all the characters on the keyboard, and therefore is more difficult to break.

e) The group should use commercial encryption software.

(The answer is on p. 2 of the PDF.)

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