Coworkers Fang, Gan, Hua, Ji, and Kun must complete three new projects: a brochure, a report, and a spreadsheet. Each...

Owning The Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

• Fang is friends with everyone, so must be assigned alone to a project.
• Kun has only one friend, Fang, so is free to work with any of Gan, Hua, or Ji.
• The restriction that only one person (not Hua) can do the spreadsheet means Fang, Gan, Ji, or Kun must do it alone.
• Only four pairs among the workers are not friends (Gan-Ji, Gan-Kun, Hua-Kun, Ji-Kun), so possible teams are highly limited.
• Assigning projects thus depends on both these friendship constraints and the one-person spreadsheet rule.

Step-by-Step Solution

Question 1: Conditional Assignment to Brochure

Complete Statement:

[BLANK 1] could be assigned to work on the brochure, but only if Gan is assigned to work on the [BLANK 2].

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: [BLANK 1] could be assigned to work on the brochure
  • Meaning: We're asked which worker's assignment to brochure is conditional.
  • Relation to Chart: We have to consider friendship connections, since no close friends can be assigned to the same project.
  • Important Implications: Some workers can only do brochure depending on where others are assigned due to friendship exclusions.
• Statement Breakdown 2:
  • Key Phrase: but only if Gan is assigned to work on the [BLANK 2]
  • Meaning: The assignment of [BLANK 1] is only possible for the brochure if Gan is assigned to a certain project.
  • Relation to Chart: Gan's assignment will either allow or prevent [BLANK 1] from being assigned to brochure depending on their friendship status.
  • Important Implications: We need to test each worker in [BLANK 1]'s spot and see which Gan assignment is critical for that worker to do brochure.
• What is needed: Which worker among Fang, Ji, or Kun could be assigned to the brochure, but only if Gan is assigned to a particular project.

Solution:

• Condensed Solution Implementation:
  Check which pairings are allowed by the friendship graph. Fang cannot work with anyone else (friends with all), so their assignment is not conditional. Kun is only friends with Fang, so Kun and Gan can work together. However, the statement is constructed around the conditional nature, pointing to Ji and Gan, who are not friends and can be assigned together.
• Necessary Data points:
  Friendship pairs: Fang is friends with everyone. Ji is friends with Fang and Hua. Gan and Ji are NOT friends. Gan and Kun are NOT friends.
  • Calculations Estimations:
    Check Ji on brochure: only allowed if Gan is also on brochure, since Ji and Gan are not friends and can both be on brochure without violating constraints. Ji's ability to be on brochure critically depends on Gan's assignment.
  • Comparison to Answer Choices:
    Fang can't be with any other worker. Kun's assignment doesn't create a conditional restriction. Ji's only way onto brochure is if Gan is also assigned to brochure.

FINAL ANSWER Blank 1: Ji

Question 2: Gan's Project Required for Ji on Brochure

Complete Statement:

Ji could be assigned to work on the brochure, but only if Gan is assigned to work on the [BLANK 2].

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: Ji could be assigned to work on the brochure
  • Meaning: Ji's assignment to brochure is under consideration.
  • Relation to Chart: Possible as long as Ji doesn't have to work with a friend (Fang or Hua).
• Statement Breakdown 2:
  • Key Phrase: but only if Gan is assigned to work on the [BLANK 2]
  • Meaning: Gan's assignment is the key enabler for Ji's assignment.
  • Relation to Chart: Ji and Gan are not friends, so they are allowed to work together on a project.
• What is needed: Which project Gan must be assigned to, in order for Ji to be able to work on the brochure.

Solution:

• Condensed Solution Implementation:
  Since Gan and Ji are not friends, the only project Gan must be on to allow Ji on brochure is brochure itself. This is the only way Ji can work on brochure given the constraints.
• Necessary Data points:
  Gan and Ji are not friends, so a shared assignment is allowed.
  • Calculations Estimations:
    Only if Gan is on brochure, Ji can also be on brochure. Other assignments for Gan do not enable Ji onto brochure.
  • Comparison to Answer Choices:
    Possible Gan assignments are brochure, report, spreadsheet. Only brochure fits the required conditional for Ji.

FINAL ANSWER Blank 2: brochure

Summary

Ji could be assigned to the brochure, but only if Gan is also assigned to the brochure. No such conditional applies for Fang or Kun; Fang cannot work with any co-worker, and Kun's assignment isn't conditional on Gan. The answer follows from the friendship graph and the exclusivity constraint: since Ji and Gan are not friends, they can be in the same assignment, allowing this conditional. Thus, the fill is 'Ji' and 'brochure'.

Question Independence Analysis

The blanks are dependent. Selecting Ji for Blank 1 establishes the relevant friendship and exclusivity constraints, making 'brochure' the unique suitable answer for Blank 2. Blank 2 cannot be determined without the answer to Blank 1.