MCAT Critical Analysis and Reasoning Skills Practice Test 6

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People's facility with numbers ranges from the aristocratic to the Ramanujanian, but it's an unfortunate fact that most are on the aristocrats' side of our old Mainer. I'm always amazed and depressed when I encounter students who have no idea what the population of the United States is, or the approximate distance from coast to coast, or roughly what percentage of the world is Chinese. I sometimes ask them as an exercise to estimate how fast human hair grows in miles per hour, or approximately how many people die on earth each day, or how many cigarettes are smoked annually in this country. Despite some initial reluctance (one student maintained that hair just doesn't grow in miles per hour), they have often improved their feel for numbers dramatically.

Without some appreciation of common large numbers, it's impossible to react with the proper skepticism to terrifying reports that more than a million American kids are kidnapped each year, or with the proper sobriety to a warhead carrying a megaton of explosive power-the equivalent of a million tons (or two billion pounds) of TNT.

And if you don't have some feeling for probabilities, automobile accidents might seem like a relatively minor problem of local travel, whereas being killed overseas by terrorists might seem to be a major risk when going overseas. As often observed, however, the 45,000 people killed annually on American roads are approximately equal to all American dead in the Vietnam War. On the other hand, the seventeen Americans killed by terrorists in 1985 were among the 28 million of us who traveled abroad that year-that's one chance in 1.6 million of becoming a victim. Compare that with these annual rates in the United States: one chance in 68,000 of choking to death; one chance in 75,000 of dying in a bicycle crash; one chance in 20,000 of drowning; and one chance in 5,300 of dying in a car crash.

Confronted with these large numbers and with the correspondingly small probabilities associated with them, the innumerate will invariably respond with the non sequitur, "Yes, but what if you're that one," and then nod knowingly, as if they've demolished your argument with their penetrating insight. This tendency to personalize is, as we'll see, a characteristic of many people who suffer from innumeracy. Equally typical is a tendency to equate the risk from obscure and exotic malady with the chances of suffering from heart and circulatory disease, from which about 12,000 Americans die each week.

There's a joke I like that is marginally relevant. An old married couple in their nineties contact a divorce lawyer, who pleads with them to stay together. "Why get divorced now after seventy years of marriage? Why not last it out? Why now?" The little old lady finally pipes up in a creaky voice: "We wanted to wait until the children were dead."

A feeling for what quantities or time spans are appropriate in various contexts is essential to getting the joke. Slipping between millions and billions or between billions and trillions should in the sense be equally funny, but it isn't, because we too often lack an intuitive feeling for these numbers. Many educated people have little grasp for these numbers and are even unaware that a million is 1,000,000; a billion is 1,000,000,000; and a trillion, 1,000,000,000,000.

A recent study by Drs. Kronlund and Phillips of the University of Washington showed that most doctors' assessments of the risks of various operations, procedures, and medications (even in their own specialties) were way off the mark, often by several orders of magnitude. I once had a conversation with a doctor who, within approximately twenty minutes, stated that a certain procedure he was contemplating (a) had a one-chance-in-a-million risk associated with it; (b) was 99 percent safe; and (c) usually went quite well. Given the fact that so many doctors seem to believe than there must be at least eleven people in the waiting room if they're to avoid being idle, I'm not surprised at this new evidence for their innumeracy.

Material used in this particular passage has been adapted from the following source:

J.A. Paulos, Innumeracy: Mathematical Illiteracy and Its Consequences. © 1988 by Collins Publishers.

1. Which of the following best describes the author's primary purpose?

  • A. To explain the causes of innumeracy and provide options on how to prevent it
  • B. To demonstrate that Americans are, on the whole, undereducated
  • C. To provide data concerning probabilities of various causes of death
  • D. To describe innumeracy and some of its consequences

2. It can be inferred that, as used in paragraph 1, the term aristocratic:

  • A. describes individuals with better-than-average mathematical skill.
  • B. refers to the traditional ruling class.
  • C. represents people with only a limited facility with numbers.
  • D. refers to an inability to understand the difference between a million and a billion.

3. The author would most likely agree with which one of the following statements?

  • A. A megaton describes an unimpressive amount of explosive power.
  • B. It is unlikely that more than a million American children are kidnapped each year.
  • C. Driving an automobile is less dangerous than swimming.
  • D. Numbers such as a billion or a trillion are often amusing.

4. Which of the following, according to the passage, may characterize the innumerate?

I. Inability to improve their understanding of numbers

II. Personalizing improbable but tragic outcomes

III. Inaccurate assessments of the probabilities of possible outcomes of medical procedures

  • A. I only
  • B. II only
  • C. I and III
  • D. II and III

5. The author most likely included the joke about the old married couple in order to:

  • A. provide further evidence of innumeracy in the elderly.
  • B. argue that couples in their nineties should not seek divorce.
  • C. illustrate the significance of an understanding of apt quantities based on context.
  • D. further support a point made in paragraph 3.

6. Which of the following is NOT included as evidence of innumeracy among doctors?

  • A. Personal experience in the form of an anecdote
  • B. Statistics regarding the frequency of death due to heart disease
  • C. Recent academic research
  • D. A humorous exaggeration of a common experience