At a certain company during Year Y, exactly six company employees transferred to the accounting department from another department, and...
GMAT Two Part Analysis : (TPA) Questions
At a certain company during Year Y, exactly six company employees transferred to the accounting department from another department, and exactly four employees transferred out of the accounting department to another department. Also during Year Y, the company hired some new employees for the accounting department, and some accounting-department employees left the company. At the end of Year Y, there were exactly five more employees in the accounting department than there were at the beginning of the year.
For this company's accounting department during Year Y, select for Newly hired and for Left a number of newly hired employees and a number of employees who left, respectively, that are jointly consistent with the information provided. Make only two selections, one in each column.
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.