At a certain company during Year Y, exactly six company employees transferred to the accounting department from another department, and...

Phase 1: Owning the Dataset

Visual Representation - Employee Flow Timeline

Let's track the accounting department's employee changes during Year Y:

Start of Year Y                                              End of Year Y
     S employees ----[Changes during Year Y]----> S + 5 employees
                         |
                         +6 (transfers IN)
                         -4 (transfers OUT)
                         +H (newly hired)
                         -L (left company)

Given Information:

• Transfers IN to accounting from other departments: 6 employees
• Transfers OUT of accounting to other departments: 4 employees
• Net change in accounting department: +5 employees
• We need to find: Newly hired (H) and Left company (L)

Phase 2: Understanding the Question

Setting Up the Equation

Let's denote:

• S = Starting number of employees in accounting
• H = Number newly hired
• L = Number who left the company

The equation for total change:

\(\mathrm{Ending\,employees = Starting\,employees + All\,changes}\)
\(\mathrm{S + 5 = S + 6 - 4 + H - L}\)

Simplifying:

\(\mathrm{S + 5 = S + 2 + H - L}\)
\(\mathrm{5 = 2 + H - L}\)
\(\mathrm{3 = H - L}\)

Key Insight: We need \(\mathrm{H - L = 3}\), meaning newly hired must exceed those who left by exactly 3.

Phase 3: Finding the Answer

Checking Answer Choices

Available choices: [2, 3, 5, 9, 14]

We need pairs where H - L = 3:

If H = 2: L would need to be -1 (impossible - can't have negative employees leaving)
If H = 3: L would need to be 0 (not in our choices)
If H = 5: L would need to be 2 checkmark (2 is in our choices!)
If H = 9: L would need to be 6 (not in our choices)
If H = 14: L would need to be 11 (not in our choices)

Stop here - we found our answer.

Verification

Let's verify: 5 newly hired - 2 left = 3
Total change: \(\mathrm{+6\,(transfers\,in) - 4\,(transfers\,out) + 5\,(newly\,hired) - 2\,(left) = +5}\) checkmark

Phase 4: Solution

Final Answer:

• Newly hired: 5
• Left: 2

These values satisfy our requirement that H - L = 3 and produce the net increase of 5 employees in the accounting department.