Self-study
Politician: The current crisis in mathematics education must be overcome if we are to remain competitive in the global economy. ███████████ ████ ██████ ████████ ███ ██████████ ██ ██████████ ████████ ████████ ██ ██████ ██ ████████ █ ███████ ███ ███████ ████ ████ ███ ███ ████████ ██ █████ █ ███████████ ██████ ██ ████ ███████ ██ █████ ████████ ████ ████████
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.
23.
Which one of the following ██████████ ███████ █████████ ████ ███ ██████████ ██████
a
If students spend █ ███████████ ██████ ██ ████ ███████ ██ █████ ████████ ████████████ ███ ███████ ██████ ██ ███████████ █████████ ████ ██ █████████
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 ██ ███████████ █████████ ████ ███ ██ ████████ ██████ ████████ █████ █ ███████████ ██████ ██ ████ ███████ ██ █████ ████████ ████████████
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 ██ █████████ ██ ███████████ ██ ███ ██████ ██ ██████ ███████████ ██ ███ ██████ ████████
This could be false. The stimulus does not talk about the relative importance of other subjects.
d
Only if we ███████ ██ █████████ ███████████ ██ ███ ██████ ███████ ████ ████████ █████ █ ███████████ ██████ ██ ████ ███████ ██ █████ ████████ ████████████
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 ███████████ ██████ ██ ████ ███████ ██ █████ ████████ ███████████ █████ ████ ██ ██ ██████ ███████████ ██ ███ ██████ ████████
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.”