A
These witnesses were more observant about details than were most of the other witnesses.
B
These witnesses had better memories than did most of the other witnesses.
C
These witnesses were less inclined than most of the other witnesses to be influenced in their testimony by the nature of the questioning.
D
These witnesses were unclear about the details at first but then began to remember more accurately as they answered questions.
E
These witnesses tended to give testimony containing more details than most of the other witnesses.
Politician: The current crisis in mathematics education must be overcome if we are to remain competitive in the global economy. Alleviating this crisis requires the employment of successful teaching methods. No method of teaching a subject can succeed that does not get students to spend a significant amount of time outside of class studying that subject.
Summary
The stimulus can be diagrammed as follows:
Notable Valid Inferences
If we are to remain competitive in the global economy, we must get students to study math outside of class.
If we are to overcome the crisis in math education, we must get students to study math outside of class.
If students don’t spend a significant amount of time studying math outside of class, then we won’t remain competitive in the global economy.
A
If students spend a significant amount of time outside of class studying mathematics, the current crisis in mathematics education will be overcome.
This could be false. Spending a significant time outside of class studying math is a necessary condition, not a sufficient condition, of resolving the crisis.
B
The current crisis in mathematics education will not be overcome unless students spend a significant amount of time outside of class studying mathematics.
This must be true. As shown in the diagram, by chaining conditional claims, we see that studying math outside of class is a necessary condition of overcoming the crisis
C
Few subjects are as important as mathematics to the effort to remain competitive in the global economy.
This could be false. The stimulus does not talk about the relative importance of other subjects.
D
Only if we succeed in remaining competitive in the global economy will students spend a significant amount of time outside of class studying mathematics.
This could be false. Remaining competitive in the global economy is a sufficient condition, not a necessary condition, of spending a lot of time studying math outside of class.
E
Students’ spending a significant amount of time outside of class studying mathematics would help us to remain competitive in the global economy.
This could be false. We know that spending lots of time outside of class studying math is a necessary condition of remaining competitive. However, that’s not logically the same as “helping.”