Friday, December 27, 2013

Numbers and Percentages Problem Set Answer Key


All answer keys in this book indicate the source of the question by giving the month and year the LSAT
was originally administered, the Logical Reasoning section number, and the question number within that
section. Each LSAT has two Logical Reasoning sections, and so the Section 1 and Section 2 designators
will refer to the first or second Logical Reasoning section in the test, not the physical section number of the
booklet.
Question #1. Flaw-#%. December 2003 LSAT, Section 1, #12. The correct answer choice is (D)
The politician’s argument is that the claims that price increases have averaged less than 3 percent are
wrong, and in support of that position the politician cites several examples of price increases, each of
which is greater than 3 percent. As mentioned in one of the chapter sidebars, “an average is a composite
number, and within the average there can be a significant degree of variation and no single entity need
embody the exact characteristic of the average (for example, the average weight of a 1 pound rock and a
99 pound rock is 50 pounds).” In making the argument, the politician has focused in on several individual
examples while ignoring the fact that an average is a compilation of many different numbers. Answer
choice (D) perfectly captures the essence of this sampling error.
Answer choice (A): The argument does not contain a source or ad hominem attack. Simply stating that a
position is wrong is different than criticizing the character of that person.
Answer choice (B): To properly claim that the economists are wrong does not require showing that they
are not pricing experts, and hence this answer is incorrect
Answer choice (C): The politician attempts to refute the position by providing evidence about large price
increases for certain products. This process, which involves facts, is different than inferring that a claim is
false because it has not been shown to be true. This answer choice would better describe an argument such
as the following: “you have not proven that God exists, so there must be no God.”
Answer choice (D): This is the correct answer. Citing several examples to refute an average is a doomed
strategy.
Answer choice (E): There is no appeal to emotion present; percentages are used to make the argument.
Question #2. Must-#%. December 1995 LSAT, Section 2, #24. The correct answer choice is (E)
The situation in Ditrama is as follows:
Under the federal revenue-sharing plan, each region receives a share of federal revenues equal to
the share of the total population of Ditrama residing in that region, as shown by a yearly
population survey.
Last year, the percentage of federal revenues Korva received for its share decreased somewhat
even though the population survey on which the revenue-sharing was based showed that Korva’s
population had increased.
If the total population of Korva increased but at the same time they experienced a decrease in revenue
allocation, the only possible solution is that the total population of Ditrama increased by more than the
Korva increase. Thus, you must seek an answer that indicates that the total population increased more than
Korva’s population increased. But be careful: this question is one of high difficulty, and the test makers do
not make it easy to spot the correct answer.
Answer choice (A): Either Mitro or Guadar could have a smaller number of residents than Korva.
Answer choice (B): This answer is impossible to prove because we do not have information about the
population growth of Korva in the years prior to the last one.
Answer choice (C): This is the most popular wrong answer choice. The key error is the claim that “Mitro
and Guadar each increased by a percentage that exceeded” Korva’s increase. Although it must be true that
at least one exceeded Korva’s increase, it does not have to be true that both exceeded Korva, as shown by
the following example:

                             Before After                (Last Year)
Total Population of Ditrama            30 (100%)                100 (100%)
Population of Korva                  10 (33%)                  15 (15%)
(people/percent of total)
Population of Mitro                   10 (33%)                  10 (10%)
(people/percent of total)
Population of Guadar                  10 (33%)                  75 (75%)
(people/percent of total)
In the example above, only one of the other regions had a population increase that exceeded Korva; the
other did not. Hence this answer choice is incorrect. Note also that this example disproves answer choice
(A) as well.
Answer choice (D): As shown by the previous example, this answer is incorrect.
Answer choice (E): This is the correct answer. From the stimulus we know that Korva had a population
increase, but a revenue drop. So, the total population of Ditrama must have increased by more than
Korva’s increase, and for this to happen, at least one other country must have had an increase in population
that exceeded Korva’s.
Note that the scenario in answer choice (C) would force answer choice (E) to be correct, and based on the
Uniqueness Rule of Answer Choices, answer (C) is incorrect for that reason alone.
Question #3. Assumption-#%. September 1995 LSAT, Section 1, #14. The correct answer choice
is (D)
This is a challenging question. The author makes the following argument:
Premise: In 1980, Country A had a per capita gross domestic product (GDP) that was $5,000
higher than that of the European Economic Community.
Premise: By 1990, the difference, when adjusted for inflation, had increased to $6,000.
Premise: A rising per capita GDP indicates a rising average standard of living.
Conclusion: The average standard of living in Country A must have risen between 1980 and 1990.
The author has fallen into the trap of believing that an increase in the difference between GDP’s means
that the actual GDP of Country A has increased. Since that is not necessarily the case based on the
number, you should look for the answer that assumes the total GDP of country A has not decreased.
Answer choice (A): The stimulus is clear that the GDP is a “per capita” (per person) figure. Hence, the
author does not need to make an assumption regarding actual population increases.
Answer choice (B): The author does need to assume this is true because a bigger GDP gap does not prove
that either must have fallen; the actual GDP of both Country A and the European Economic Community
(EEC) could rise and the author’s argument would still be valid.
Answer choice (C): In the argument the author uses the GDP of the entire EEC. Since the figure for the
EEC would necessarily be an average drawn from the numbers of multiple countries, the author does not
need to make any assumptions about figures for individual countries within the EEC.
Answer choice (D): This is the correct answer. In order to conclude that an increasing difference in GDP
translates to an actual increase in GDP, the author must assume that the GDP of the point of comparison,
the EEC, did not fall dramatically. Consider the following example, which assigns actual numbers to the
GDP of each group in 1980, and then shows a variety of possibilities for the numbers in 1990:
                 1980   #1: 1990   #2: 1990   #3: 1990   #4: 1990
GDP of Country A     105    107         156       96          105
GDP of the EEC       100    101         150       90          99
Difference              +5    +6          +6       +6         +6
Each of the four examples for 1990 is consistent with the claim that there is a $6000 difference between
the GDP of Country A and the GDP of the EEC. The first two examples for 1990, #1 and #2, show that
the total GDP of Country A, and therefore the standard of living as defined in the stimulus, has risen.
Example #3, shows that even though the gap has increased between the two groups, the actual GDP of
Country A has decreased, and therefore the standard of living in Country A has decreased. This is
inconsistent with the author’s conclusion, so the author must be assuming that this type of scenario cannot
occur. In example #4, we see a second example that is incompatible with the author’s conclusion, one
where the gap remains at $600, but the GDP of Country A remains the same. The author must assume that
the fourth scenario also cannot occur, and that the GDP of the EEC cannot drop by the $1000 that is the
amount of the increase in the gap. Hence, the author must assume that if the GDP of the EEC drops, it
drops by less than $1000, and therefore answer choice (D) is correct.
This is clearly a confusing answer, but do not forget that you can always apply the Assumption Negation
Technique to any answer choice in an Assumption question. Answer choice (D), when negated, reads:
“The per capita GDP of the European Economic Community was lower by more than $1,000 in 1990
than it had been in 1980.” This negation would definitely weaken the argument because it would create a
scenario like #3 or one even worse than #4. Because the answer choice weakens the argument when
negated, it must be the correct answer.
Answer choice (E): This answer is incorrect for the same reason cited in answer choice (C): since the
figure for the EEC would necessarily be an average drawn from the numbers of multiple countries, the
author does not need to make any assumptions about the figures for individual countries within the EEC,
regardless of year.
Question #4. Must-#%. September 1995 LSAT, Section 1, #20. The correct answer choice is (E)
The stimulus does not contain a conclusion, but it does contain an interesting fact set:
“Students from outside the province of Markland, who in any given academic year pay twice as
much tuition each as do students from Markland, had traditionally accounted for at least two-thirds
of the enrollment at Central Markland College.”
This sentence indicates that the non-Marklanders are paying a greater amount of tuition, and they
previously accounted for at least 66% of the enrollment. This statement is followed by:
“Over the past 10 years academic standards at the college have risen, and the proportion of
students who are not Marklanders has dropped to around 40 percent.”
This sentence can be deceptive because it contains two ideas that are unrelated and many people assume
that the proportion of non-Marklanders has dropped because the academic standards rose. The sentence
only states that the non-Marklanders have dropped, not that they dropped because of the raised standards.
As you learned from our discussion in this chapter, the fact that the non-Marklanders have dropped in
percent does not mean that their actual number has decreased (Misconception #2). The following is an
example of how the percent could decrease while numbers could increase:
                            10 years ago           Today
Total number of students            100                200
at Central Markland
Number of non-Markland            66 (66%)           80 (40%)
students
(people/percent of total)
Number of Markland students          34 (34%)          120 (60%)
(people/percent of total)
Answer choice (A): The stimulus does not cite any reason for why or how the academic standards were
increased, so this answer is incorrect.
Answer choice (B): This answer tests your ability to understand the last sentence of the stimulus. As
discussed above, the last sentence does not provide a reason for the decline in non-Markland students, so
removing the stipulation about the rise in academic standards would not tell us whether non-Marklanders
would still be enrolled in the college.
Answer choice (C): This is a difficult answer. If the size of the college stayed the same, then this answer
would be correct. But, as shown by the example above, the statement in this answer does not have to be
true when the total size of the college changes. In the example, both Markland students and non-Markland
student numbers grew.
Answer choice (D): Remember, this is a Must Be True question, so every answer must pass the Fact Test.
No information was given about other Markland colleges, so this answer is incorrect.
Answer choice (E): This is the correct answer. If the college’s per capita revenue from tuition remains
constant while at the same time the high-tuition paying non-Marklanders have decreased in percentage, the
college must have derived new tuition revenue by raising tuition. In other words, when the percentage of
non-Marklanders drops, the average tuition per person must also drop because they pay twice as much as
the Markland students. In order to keep the per person revenue the same, fees would have to be raised.

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