You are given five statements about starting salaries of teachers and other professionals, age of first year teachers, and the relationship between education and salary. Each option lists a set of three of these statements. Identify the set of statements that is logically consistent and best fits together: (a) the gap between starting salaries has shrunk, (b) the average age of first year teachers is the same as in 1975, (c) starting teachers are no longer underpaid, (d) the extent of formal education helps determine salary level, and (e) starting salaries of other professionals have increased by twenty percent in recent years.

Introduction / Context:
This question asks you to identify which set of three statements about starting salaries of teachers and other professionals is logically consistent. The statements discuss how the salary gap has changed, how much other professionals salaries have increased, whether starting teachers are underpaid, the role of formal education, and the age of first year teachers. Instead of choosing a single statement that follows from others, we are asked to select the group of three that fits together most coherently without contradiction and that presents a meaningful picture about teacher pay relative to other professionals.

Given Data / Assumptions:

• Statement a: The gap between average starting salaries of teachers and those of other professionals has shrunk in recent years.
• Statement b: The average age of first year teachers is the same as it was in 1975.
• Statement c: Starting teachers are no longer underpaid.
• Statement d: The extent of a person formal education is a measure by which to determine salary level.
• Statement e: Over the last few years, average starting salaries of other professionals have increased by twenty percent.
• We assume teachers generally have education comparable to that of other professionals.

Concept / Approach:
To judge logical consistency in this context, we ask whether the statements in a given set can all be true at the same time and whether they combine to form a sensible picture about teacher pay. The best set will be the one where the statements reinforce each other rather than being unrelated or suggesting unresolved tension. We check each option by seeing how its three statements interact when taken together, particularly with respect to whether teachers remain underpaid relative to other professionals.

Step-by-Step Solution:
Step 1: Analyse the relation between a, e, and c. Statement e says other professionals starting salaries rose by twenty percent. If, despite this, statement a claims that the salary gap between teachers and others has shrunk, then teachers starting salaries must have increased by more than twenty percent, helping to remove earlier underpayment. Statement c explicitly concludes that starting teachers are no longer underpaid. All three statements therefore support a coherent scenario: teachers were underpaid earlier, but larger recent increases in teacher salaries, relative to those of other professionals, have reduced the gap and removed underpayment.Step 2: Examine sets involving d and b. Statement d introduces a general rule that education determines salary level. Statement b talks about age of first year teachers, which has no direct impact on whether they are underpaid or whether the gap has changed. Thus sets with b and d tend to be less focused on explaining changes in underpayment or salary gap.Step 3: Consider option c, which uses a, c, and b. Here, a and c do fit together, but b about age is largely irrelevant to the theme of fairness and salary gap. This set is consistent but does not explain why teachers are no longer underpaid as clearly as the combination of a, e, and c.Step 4: Notice that option a and option b effectively mention the same three statements in a different order, neither of which includes c, which is the direct statement about underpayment.Step 5: Since a coherent and focused picture emerges most strongly from combining a, e, and c, option d, which chooses this set, is the best answer.

Verification / Alternative check:
Imagine the situation described by statements a, e, and c numerically. If other professionals saw a twenty percent rise, and yet the gap between their starting salaries and those of teachers shrank, it means that teachers pay must have risen by more than twenty percent. That greater increase can plausibly move teachers from being underpaid to not underpaid, matching statement c. The three statements therefore form a logically consistent narrative: teachers were underpaid earlier, significant recent increases in their salaries have shrunk the gap and removed the underpayment.

Why Other Options Are Wrong:

• Options a and b involve statements e, b, and d. These can be true together, but they do not directly address or explain whether teachers remain underpaid. They lack the clear link that c provides.
• Option c uses a, c, and b. While these can be consistent, the presence of b adds no explanatory power, and the absence of e makes it harder to understand how the gap shrank.
• Option e claims that none of the sets is consistent, which is incorrect because a, e, and c clearly support each other.

Common Pitfalls:
Students often treat logical consistency as meaning merely that statements are not explicitly contradictory, rather than also considering how well they fit together to explain a situation. Another pitfall is ignoring the numerical information in statement e and how it interacts with the shrinking gap in statement a. Recognising that a, e, and c combine to tell a coherent story about improved teacher pay allows us to see why option d is the most suitable choice.

Final Answer:
Statements a, e, and c taken together form a logically consistent set.