At XYZ Inc., an employee receives a verbal warning upon accumulating at least 3 unexcused absences within any 365-day period...

GMAT Two Part Analysis : (TPA) Questions

Source: Official Guide

Two Part Analysis

Quant - Advanced

HARD

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Notes

Post a Query

At XYZ Inc., an employee receives a verbal warning upon accumulating at least 3 unexcused absences within any 365-day period and a written reprimand upon accumulating at least 4 such absences. For any single 8-hour workday, missing between 10 minutes and 2 hours of work counts as one-third of an absence, missing between 2 hours and 4 hours of work counts as half an absence, and missing more than 4 hours counts as a full absence. However, an employee may stay late to make up for up to 1 hour of an unexcused absence on the same day.

The table contains descriptions of the unexcused absences of 5 employees of XYZ Inc. Assume that in each case the employee had no other unexcused absences and made up no other time. In the table, select a description of an employee who qualified for a verbal warning but not a written reprimand, and select a description of an employee who qualified for a written reprimand. Make only two selections, one in each column.

Verbal warning

Written reprimand

Absent all day on 5 April 2010, 8 June 2010, 17 April 2011, and 14 June 2011

Absent 4.5 hours but stayed 1 hour late on May 13 May 2010; absent all day on 2 June 2010, 1 May 2011, and 21 July 2011

Absent 4.5 hours on 19 March 2010; stayed 1 hour late on 20 March 2010; absent all day on 8 and 9 February 2011; arrived 40 minutes late on 17 April 2011

Absent 3.5 hours on 13 September 2010; absent 1 hour on 15 September 2010; absent 6 hours on 16 September 2010; absent 2.5 hours on 18 September 2010; absent 1 hour on 19 September 2010

Absent 3 hours on 7 July 2010; absent 2.5 hours on 13 September 2010; absent all day on 31 January 2011 and 4 July 2011; absent 5 hours on 12 March 2011

Solution

Phase 1: Owning the Dataset

Understanding the Rules

Thresholds:

Verbal warning: \(\geq 3\) absences within any 365-day period
Written reprimand: \(\geq 4\) absences within any 365-day period

Absence Counting:

Time Missed	Counts As
10 minutes - 2 hours	\(\frac{1}{3}\) absence
2 hours - 4 hours	\(\frac{1}{2}\) absence
More than 4 hours	1 full absence

Make-up rule: Can stay late to make up for up to 1 hour on the same day.

Phase 2: Understanding the Question

We need to find:

One employee who qualified for verbal warning (\(\geq 3\)) but NOT written reprimand (\(< 4\))
One employee who qualified for written reprimand (\(\geq 4\))

Phase 3: Finding the Answer

Let's analyze each employee systematically:

Employee 1: "Absent all day on 5 April 2010, 8 June 2010, 17 April 2011, and 14 June 2011"

4 full-day absences = 4 full absences
Within any 365-day period: Maximum is 2 absences (dates are spread out)
Result: No warning

Employee 2: "Absent 4.5 hours but stayed 1 hour late on May 13 May 2010; absent all day on 2 June 2010, 1 May 2011, and 21 July 2011"

May 13, 2010: \(4.5 - 1 = 3.5\) hours = \(\frac{1}{2}\) absence
June 2, 2010: 1 full absence
May 1, 2011: 1 full absence
July 21, 2011: 1 full absence
Within 365-day period (May 13, 2010 to May 12, 2011): \(0.5 + 1 + 1 = 2.5\) absences
Result: No warning

Employee 3: "Absent 4.5 hours on 19 March 2010; stayed 1 hour late on 20 March 2010; absent all day on 8 and 9 February 2011; arrived 40 minutes late on 17 April 2011"

March 19, 2010: 4.5 hours = 1 full absence
March 20, 2010: stayed late (no absence to make up) = 0
Feb 8, 2011: 1 full absence
Feb 9, 2011: 1 full absence
April 17, 2011: 40 minutes = \(\frac{1}{3}\) absence
Within 365-day period (March 19, 2010 to March 18, 2011): \(1 + 1 + 1 = 3\) absences
Result: Verbal warning (\(\geq 3\)) but NOT written reprimand (\(< 4\)) ✓

Employee 4: "Absent 3.5 hours on 13 September 2010; absent 1 hour on 15 September 2010; absent 6 hours on 16 September 2010; absent 2.5 hours on 18 September 2010; absent 1 hour on 19 September 2010"

Sept 13: 3.5 hours = \(\frac{1}{2}\) absence
Sept 15: 1 hour = \(\frac{1}{3}\) absence
Sept 16: 6 hours = 1 full absence
Sept 18: 2.5 hours = \(\frac{1}{2}\) absence
Sept 19: 1 hour = \(\frac{1}{3}\) absence
Total: \(0.5 + \frac{1}{3} + 1 + 0.5 + \frac{1}{3} = 2.67\) absences
Result: No warning

Employee 5: "Absent 3 hours on 7 July 2010; absent 2.5 hours on 13 September 2010; absent all day on 31 January 2011 and 4 July 2011; absent 5 hours on 12 March 2011"

July 7, 2010: 3 hours = \(\frac{1}{2}\) absence
Sept 13, 2010: 2.5 hours = \(\frac{1}{2}\) absence
Jan 31, 2011: 1 full absence
July 4, 2011: 1 full absence
March 12, 2011: 5 hours = 1 full absence
Within 365-day period (Sept 13, 2010 to Sept 12, 2011): \(0.5 + 1 + 1 + 1 = 4\) absences
Result: Written reprimand (\(\geq 4\)) ✓

Phase 4: Solution

Final Answer:

Verbal warning: Employee 3 (3 absences in 365-day period)
Written reprimand: Employee 5 (4 absences in 365-day period)

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