A private contractor completed three projects (Projects A-C) last month. For each of those three projects, she completed the following...

SOLUTION

OWNING THE DATASET

Project A: Step 1 → Step 2 → Step 3 → Step 4
Project B: Step 1 → Step 2 → Step 3 → Step 4
Project C: Step 1 → Step 2 → Step 3 → Step 4

1. Step 1 of B > Step 2 of A (\(\mathrm{B1}\) comes after \(\mathrm{A2}\))
2. Step 1 of C > Step 3 of B (\(\mathrm{C1}\) comes after \(\mathrm{B3}\))
3. Project B completed last (\(\mathrm{B4} > \mathrm{A4}\) and \(\mathrm{B4} > \mathrm{C4}\))

• Since \(\mathrm{B1} > \mathrm{A2}\), and steps within each project are sequential: \(\mathrm{A1} < \mathrm{A2} < \mathrm{B1} < \mathrm{B2} < \mathrm{B3}\)
• Since \(\mathrm{C1} > \mathrm{B3}\): \(\mathrm{B3} < \mathrm{C1} < \mathrm{C2} < \mathrm{C3} < \mathrm{C4}\)
• Since Project B completed last: Both \(\mathrm{A4}\) and \(\mathrm{C4}\) must occur before \(\mathrm{B4}\)

SEEKING THE CRITICAL INSIGHT

This is an ordering problem. The critical insight is that the constraints create a chain of dependencies that determines the relative order of the mentioned steps.

UNDERSTANDING THE QUESTION

We need to order these five steps:

• Step 1 of Project B (\(\mathrm{B1}\))
• Step 2 of Project A (\(\mathrm{A2}\))
• Step 3 of Project A (\(\mathrm{A3}\))
• Step 4 of Project B (\(\mathrm{B4}\))
• Step 4 of Project C (\(\mathrm{C4}\))

PROCESSING THE SOLUTION

From constraint 1: \(\mathrm{A2} < \mathrm{B1}\)
- This immediately tells us \(\mathrm{A2}\) comes before \(\mathrm{B1}\)

From constraint 3: \(\mathrm{B4}\) is the last project completed
- This means \(\mathrm{B4} > \mathrm{A4}\) and \(\mathrm{B4} > \mathrm{C4}\)
- Among our choices, \(\mathrm{B4}\) must come after \(\mathrm{C4}\)

For \(\mathrm{A3}\):
- Within Project A: \(\mathrm{A2} < \mathrm{A3} < \mathrm{A4}\)
- So \(\mathrm{A3}\) comes after \(\mathrm{A2}\)

Among the five mentioned steps:

1. \(\mathrm{A2}\) comes first - It must precede \(\mathrm{B1}\) by constraint
2. \(\mathrm{A3}\) follows \(\mathrm{A2}\) (project sequence)
3. \(\mathrm{B1}\) follows \(\mathrm{A2}\) (given constraint)
4. \(\mathrm{C4}\) comes somewhere after \(\mathrm{C1}\) (which comes after \(\mathrm{B3}\))
5. \(\mathrm{B4}\) comes last - It's after both \(\mathrm{A4}\) and \(\mathrm{C4}\) (Project B completed last)

FINAL SOLUTION SYNTHESIS

1. Identified that \(\mathrm{A2}\) must come before \(\mathrm{B1}\) (given constraint)
2. Recognized that \(\mathrm{B4}\) must come after both \(\mathrm{A4}\) and \(\mathrm{C4}\) (B is last project)
3. Among the five choices, \(\mathrm{A2}\) has no predecessor, making it First
4. Among the five choices, \(\mathrm{B4}\) has no successor, making it Last

• First: Step 2 of Project A
• Last: Step 4 of Project B

The constraints create a clear hierarchy where \(\mathrm{A2}\) anchors the beginning of the sequence among our choices, and \(\mathrm{B4}\) anchors the end. This is a deterministic result based on the given conditions.

In TPA ordering questions, quickly identify "anchor points" - steps that must come first or last based on constraints. These often directly lead to the answer without needing to work out the complete sequence.