A
Taken together, the stocks recommended on the television show performed better than the market as a whole for the past year.
B
Taken together, the stocks recommended on the television show performed better for the past 12-year period than stock portfolios that were actually selected by any other means.
C
Performance of the stocks recommended on the television show was measured by stock dividends, whereas the performance of the market as a whole was measured by change in share value.
D
Performance of the stocks recommended on the television show was measured independently by a number of analysts, and the results of all the measurements concurred.
E
The stock portfolios for which the guests were consultants performed better for the past 12-year period than the market as a whole.
A
Neither rhododendrons nor crocuses bloom for more than a few weeks each year, and the blossoms of rhododendrons growing in any area do not appear until at least several weeks after crocuses growing in that area have ceased to bloom.
B
Many people find it unpleasant to be outdoors for long periods when the temperature is at or about 1(C.
C
The climate and soil conditions that favor the growth of rhododendrons are also favorable to the growth of crocuses.
D
Air temperature surrounding rhododendrons, which can grow 12 feet tall, is likely to differ from air temperature surrounding crocuses, which are normally only a few inches high, by more than 2(C, even if the two plants are growing side by side.
E
Certain types of thermometers that are commonly used to measure outdoor temperatures can be extremely accurate in moderate temperature ranges but much less accurate in warmer or colder temperature ranges.
The mayor, an outspoken critic of the proposed restoration of city hall, is right when he notes that the building is outdated, but that the restoration would be expensive at a time when the budget is already tight. We cannot afford such a luxury item in this time of financial restraint, he says. However, I respectfully disagree. The building provides the last remaining link to the days of the city’s founding, and preserving a sense of municipal history is crucial to maintaining respect for our city government and its authority. So to the question, “Can we really afford to?” I can only respond, “Can we afford not to?”
A
The argument is solely an emotional appeal to history.
B
The argument ambiguously uses the word “afford.”
C
The argument inappropriately appeals to the authority of the mayor.
D
The argument incorrectly presumes that the restoration would be expensive.
E
The argument inappropriately relies on the emotional connotations of words such as “outdated” and “luxury.”
Paul: I disagree. Some students forced to perform community service have enjoyed it so much that they subsequently actually volunteer to do something similar. In such cases, the policy can clearly be said to have fostered a habit of volunteering.
A
He argues that Sarah is assuming just what she sets out to prove.
B
He argues that Sarah’s conception of what it means to volunteer excludes certain activities that ought to be considered instances of volunteering.
C
He introduces considerations that call into question one of Sarah’s assumptions.
D
He questions Sarah’s motives for advancing an argument against the school policy.
E
He argues that a policy Sarah fails to consider could accomplish the same aim as the policy that Sarah considers.
If this parking policy is unpopular with the faculty, then we should modify it. If it is unpopular among students, we should adopt a new policy. And, it is bound to be unpopular either with the faculty or among students.
Summary
If the policy’s not popular with faculty, then we should modify it (or, by contrapositive, if we shouldn’t modify the policy, then it must be popular with faculty).
If the policy’s popular with faculty, it’s bound to be unpopular with students. (And if it’s popular with students, it’s bound to be unpopular with faculty. Popularity with one group implies unpopularity with the other.)
If the policy’s not popular with students, we should adopt a new policy.
Notable Valid Inferences
If we shouldn’t modify the existing policy, we should adopt a new policy.
If the policy’s popular with faculty, we should adopt a new policy.
If the policy’s popular with students, we should modify the policy.
A
We should attempt to popularize this parking policy among either the faculty or students.
The stimulus doesn’t suggest that any one scenario is more desirable than another. There’s no indication that the existing policy should be popular with either group, or that there’s something undesirable about the policy being unpopular.
B
We should modify this parking policy only if this will not reduce its popularity among students.
This says that modifying the policy is sufficient for not reducing its popularity among students. There are two problems here. First, modifying the policy isn’t sufficient for anything. Second, the policy is either popular or unpopular—there’s no “reduce popularity” condition.
C
We should modify this parking policy if modification will not reduce its popularity with the faculty.
The sufficient condition here is never addressed in the stimulus. The stimulus only considers what happens when the policy is popular or unpopular. There’s no discussion of reductions in popularity.
D
If this parking policy is popular among students, then we should adopt a new policy.
The stimulus states that if the policy is unpopular among students, then we should adopt a new policy. Meanwhile, if the policy is popular as (D) says, we can infer that we should modify the existing policy.
E
If this parking policy is popular with the faculty, then we should adopt a new policy.
If the policy is popular with faculty, then it must be unpopular with students (because it’s bound to be unpopular with at least one group). And if it’s unpopular with students, then we should adopt a new policy.
Essayist: Wisdom and intelligence are desirable qualities. However, being intelligent does not imply that one is wise, nor does being wise imply that one is intelligent. In my own experience, the people I meet have one or the other of these qualities but not both.
Summary
Wisdom and intelligence are desirable.
Someone can be intelligent, but not wise.
Someone can be wise, but not intelligent.
In the speaker’s experience, people she meets have either intelligence or wisdom, but not both.
Notable Valid Inferences
Some people do not have both intelligence and wisdom.
A
Most people are neither intelligent nor wise.
Could be true. It’s possible most, or even all people in the world do not have both wisdom and intelligence. None of the facts indicates that there must be someone who has both wisdom and intelligence.
B
Most people are both intelligent and wise.
Could be true. Although (B) would be false if it were limited to the people the stimulus’s author has met, (B) isn’t limited to those people. Most people in the world could be both — the author just hasn’t met them.
C
No one is both wise and intelligent.
Could be true. The stimulus doesn’t say anything indicating that there must be at least one person who is both wise and intelligent. It’s possible nobody has both wisdom and intelligence.
D
No one is either wise or intelligent.
Must be false. The author said she knows people who have one of the qualities of wisdom or intelligence, but not both. That means there’s at least one person out there who has wisdom or intelligence..
E
Many people are intelligent and yet lack wisdom.
Could be true. The author said she knows people who have wisdom or intelligence, but not both. It’s possible many of those people are intelligent, but don’t have wisdom.
This question presumes knowledge of these lessons on Lawgic:
https://classic.7sage.com/lesson/contrapositives-demorgans-law
https://classic.7sage.com/lesson/advanced-negate-some-statements
Don't worry if this question was tough. If you got it right, then you should feel great about yourself!
Numismatist: In medieval Spain, most gold coins were minted from gold mined in West Africa, in the area that is now Senegal. The gold mined in this region was the purest known. Its gold content of 92 percent allowed coins to be minted without refining the gold, and indeed coins minted from this source of gold can be recognized because they have that gold content. The mints could refine gold and produced other kinds of coins that had much purer gold content, but the Senegalese gold was never refined.
Summary
A numismatist tells us that most medieval Spanish gold coins were made of gold mined in Senegal. The Senegalese gold was 92 percent pure, which is so pure that it was never refined further before minting the coins. Gold from other sources, however, could be refined and thus still be minted into coins with a gold content higher than the Senegalese gold.
Strongly Supported Conclusions
The strongly supported conclusions that we can find in these facts are:
Most gold coins minted in medieval Spain had a gold content of 92 percent and were made of unrefined gold.
Medieval Spanish mints were able to refine gold from a purity less than 92 percent to a purity above 92 percent.
Some coins were minted in medieval Spain with a gold content higher than 92 percent, and were made of gold that was originally less than 92 percent pure.
A
Coins minted from Senegalese gold all contained the same weight, as well as the same proportion, of gold.
This is not supported. The stimulus never indicates the weight of different coins, only the purity of the gold used to make them. We have no idea whether all coins made from Senegalese gold had the same total weight.
B
The source of some refined gold from which coins were minted was unrefined gold with a gold content of less than 92 percent.
This is strongly supported. We know that 92 percent pure Senegalese gold, the purest known, was never refined, so any refined gold coins had to come from a less-than-92-percent pure source. And the facts state that some more-than-92-percent pure (i.e. refined) coins were made.
C
Two coins could have the same monetary value even though they differed from each other in the percentage of gold they contained.
This is not supported. The facts given don’t suggest anything about the monetary value of different coins, so we just can’t say how that relates to gold percentage.
D
No gold coins were minted that had a gold content of less than 92 percent.
This is not supported. We know that some coins were minted with a gold content of 92 percent and that some were minted with an even higher gold content, but the author never indicates whether or not coins were minted with a lower gold content.
E
The only unrefined gold from which coins could be minted was Senegalese gold.
This is not supported. Just because medieval Spanish mints made coins out of unrefined Senegalese gold, that doesn’t mean they never used other unrefined gold. Maybe they had a source of 90 percent pure gold that they also didn’t refine. We just don’t know!