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  • Question 1
    • Suppose an α-particle starting from rest is accelerated through a 5 megavolt potential difference. What is the
      final kinetic energy of the α-particle? 1

      Section: Physical Sciences 

      Answer: A
  • Question 2
    • …Until last year many people – but not most economists – thought that the economic data told a simple tale.
      On one side, productivity – the average output of an average worker – was rising. And although the rate of
      productivity increase was very slow during the 1970’s and early 1980’s, the official numbers said that it had
      accelerated significantly in the 1990’s. By 1994 an average worker was producing about 20 percent more than
      his or her counterpart in 1978.
      On the other hand, other statistics said that real, inflation- adjusted wages had not been rising at anything like
      the same rate. In fact, some of the most commonly cited numbers showed real wages actually falling over the
      last 25 years. Those who did their homework knew that the gloomiest numbers overstated the case…Still, even
      the most optimistic measure, the total hourly compensation of the average worker, rose only 3 percent between
      1978 and 1994…
      …But now the experts are telling us that the whole thing may have been a figment of our statistical
      imaginations… a blue-ribbon panel of economists headed by Michael Boskin of Stanford declared that the
      Consumer Price Index [C.P.I.] had been systematically overstating inflation, probably by more than 1 percent
      per year for the last two decades, mainly failing to take account of changes in the patterns of consumption and
      improvements in product quality…
      …The Boskin report, in particular, is not an official document – it will be quite a while before the Government
      actually issues a revised C.P.I., and the eventual revision may be smaller than Boskin and his colleagues
      propose. Still, the general outline of the resolution is pretty clear. When all the revisions are taken into account,
      productivity growth will probably look somewhat higher than it did before, because some of the revisions being
      proposed to the way we measure consumer prices will also affect the way we calculate growth. But the rate of
      growth of real wages will look much higher – and so it will now be roughly in line with productivity, which will
      therefore reconcile numbers on productivity and wages with data that show a roughly unchanged distribution of
      income between capital and labor. In other words, the whole story about workers not sharing in productivity
      gains will turn out to have been based on a statistical illusion.
      It is important not to go overboard on this point. There are real problems in America, and our previous concerns
      were by no means pure hypochondria. For one thing, it remains true that the rate of economic progress over
      the past 25 years has been much slower than it was in the previous 25. Even if Boskin’s numbers are right, the
      income of the median family – which officially has experienced virtually no gain since 1973 – has risen by only
      about 35 percent over the past 25 years, compared with 100 percent over the previous 25. Furthermore, it is
      quite likely that if we “Boskinized” the old data – that is, if we tried to adjust the C.P.I. for the 50’s and 60’s to
      take account of changing consumption patterns and rising product quality – we would find that official numbers
      understated the rate of progress just as much if not more than they did in recent decades…
      …Moreover, while workers as a group have shared fully in national productivity gains, they have not done so
      equally. The overwhelming evidence of a huge increase in income inequality in America has nothing to do with
      price indexes and is therefore unaffected by recent statistical revelations. It is still true that families in the
      bottom fifth, who had 5.4 percent of total income in 1970, had only 4.2 percent in 1994; and that over the same
      period the share of the top 5 percent went from 15.6 to 20.1. And it is still true that corporate C.E.O.’s, who
      used to make about 35 times as much as their employees, now make 120 times as much or more…
      …While these are real and serious problems, however, one thing is now clear: the truth about what is
      happening in America is more subtle than the simplistic morality play about greedy capitalists and oppressed
      workers that so many would-be sophisticates accepted only a few months ago. There was little excuse for
      buying into that simplistic view then; there is no excuse now…
      According to the passage, “Boskinization” adjusts the C.P.I. by:

      Section: Verbal Reasoning

      Answer: C
  • Question 3
    • When softball players take batting practice, they often use a machine called an “automatic pitcher,” which is
      essentially a cannon that uses air pressure to launch a projectile. In a prototype automatic pitcher, a softball is
      loaded into the barrel of the cannon and rests against a flat disk. That disk is locked into place, and a high air
      pressure is built up behind it. When the disk is released, the softball is pushed along the barrel of the cannon
      and ejected at a speed of V0.
      Figure 1 shows the batter and automatic pitcher. The angle of the barrel to the horizontal is θ. The unit vectors i
      and j point in the horizontal and vertical directions respectively.
      MCAT-part-2-page295-image73
      Figure 1
      The height above the ground y of the softball as a function of time t is shown in Figure 2, where t = 0 at Point
      A, t = tB at Point B, and t = tC at Point C. The softball is ejected from the barrel of the cannon at Point A; it
      reaches its maximum height at Point B; and the batter hits the softball at Point C. (Note: Assume that the
      effects of air resistance are negligible unless otherwise stated.)
      MCAT-part-2-page295-image72
      Figure 2
      How will V0 change if the impulse on the softball remains the same but its mass is doubled?

      Section: Physical Sciences 

      Answer: B
  • Question 4
    • Several techniques have been developed to determine the order of a reaction. The rate of a reaction cannot be
      predicted on the basis of the overall equation, but can be predicted on the basis of the rate-determining step.
      For instance, the following reaction can be broken down into three steps.
      A + D → F + G
      Step 1
      A → B + C
      (slow)
      Step 2
      B + D → E + F
      (fast)
      Step 3
      E + C → G
      (fast)
      Reaction 1
      In this case, the first step in the reaction pathway is the rate-determining step. Therefore, the overall rate of the
      reaction must equal the rate of the first step, k1 [A] where k1 is the rate constant for the first step. (Rate
      constants of the different steps are denoted by kx
      , where x is the step number.)
      In some cases, it is desirable to measure the rate of a reaction in relation to only one species. In a secondorder reaction, for instance, a large excess of one species is included in the reaction vessel. Since a relatively
      small amount of this large concentration is reacted, we assume that the concentration essentially remains
      unchanged. Such a reaction is called a pseudo first-order reaction. A new rate constant, k', is established, equal
      to the product of the rate constant of the original reaction, k, and the concentration of the species in excess.
      This approach is often used to analyze enzyme activity.
      In some cases, the reaction rate may be dependent on the concentration of a short-lived intermediate. This can
      happen if the rate-determining step is not the first step. In this case, the concentration of the intermediate must
      be derived from the equilibrium constant of the preceding step. For redox reactions, the equilibrium can be
      correlated with the voltage produced by two half-cells by means of the Nernst equation. This equation states
      that at any given moment:
      MCAT-part-1-page303-image56
      Equation 1
      When
      a A + b B → c C + d D
      Reaction 2
      Note: R = 8.314 J/K·mol; F = 9.6485 × 104 C/mol.)
      Which of the following is true of a reaction at equilibrium?
      I) k1/k−1 = 1
      II) E = E0
      III) ln([C]c [D]d /[A]a [B]b) = nFE0/RT

      Section: Physical Sciences 

      Answer: B
  • Question 5
    • The atomic size of an atom is: 

      Section: Physical Sciences 

      Answer: B
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