A retail store has 60 employees—full-time salespeople (FT sales), part-time salespeople (PT sales), and managers—in the proportions shown by the...

Owning The Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

1. The staff consists of 36 part-time salespeople, 18 full-time salespeople, and 6 managers, derived from the 60/30/10 percent split in the chart.
2. Currently, because PT sales work half as many hours as FT sales (and managers), the total weekly hours for FT sales = \(\mathrm{18h}\) (for h = weekly hours), while PT sales total = \(\mathrm{36 \times (h/2) = 18h}\). Thus, the ratio of FT:PT sales hours is \(\mathrm{1:1}\), not the desired \(\mathrm{2:3}\).
3. To achieve a \(\mathrm{2:3}\) hours ratio between FT and PT sales (keeping managers unchanged), the number of PT salespeople must be three times the number of FT salespeople. This would require adjusting the staff distribution among salespeople while maintaining the sum of FT and PT sales employees at (60 - number of managers = 54). Solving \(\mathrm{y = 3x}\) and \(\mathrm{x + y = 54}\) yields 14 FT and 42 PT salespeople—a change of reducing FT by 4 and increasing PT by 6.

Step-by-Step Solution

Question 1: Change in Full-Time Salespeople

Complete Statement:

To achieve the desired ratio, the store could [BLANK 1] the number of full-time salespeople

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: To achieve the desired ratio
    Meaning: The store wants the ratio of full-time to part-time total sales hours to become \(\mathrm{2:3}\).
    Relation to Chart: The current numbers of full-time and part-time employees are given in the chart.
    Important Implications: We need to adjust the number of employees to achieve this ratio, based on their respective working hours.
• Statement Breakdown 2:
  • Key Phrase: the number of full-time salespeople
    Meaning: This refers specifically to changing how many full-time salespeople there are.
    Relation to Chart: The chart shows there are currently 18 full-time salespeople.
    Important Implications: Any change must account for the total number of salespeople (full-time + part-time) staying constant.
• What is needed: Whether to increase or decrease the full-time salespeople, and by how many, to achieve the desired ratio while keeping the total number of non-manager employees unchanged.

Solution:

• Condensed Solution Implementation:
  Let x be the number of full-time and y the number of part-time salespeople needed to reach the \(\mathrm{2:3}\) ratio in total hours. Part-time work half the hours of full-time. For a \(\mathrm{2:3}\) ratio of full-time to part-time total hours, the number of part-time salespeople must be 3 times the number of full-time. The total number of salespeople (non-manager employees) is 54, so \(\mathrm{x + y = 54}\) and \(\mathrm{y = 3x}\).
• Necessary Data points:
  Current full-time salespeople: 18. Current part-time salespeople: 36. Total non-manager salespeople must remain at 54.
  Calculations Estimations:
  \(\mathrm{x + 3x = 54}\), so \(\mathrm{4x = 54}\), which gives \(\mathrm{x = 13.5}\). Since number of people must be integer, use 14 full-time (next closest integer). 14 full-time + 42 part-time = 56 (slightly over, but 13 full-time + 39 part-time = 52, which is too few). The best fit is 14 full-time and 42 part-time. So, decrease full-time salespeople from 18 to 14: decrease by 4.
  Comparison to Answer Choices:
  The answer that matches is 'decrease by 4'.

FINAL ANSWER Blank 1: decrease by 4

Question 2: Change in Part-Time Salespeople

Complete Statement:

and [BLANK 2] the number of part-time salespeople

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: the number of part-time salespeople
    Meaning: This refers specifically to the change in the number of part-time salespeople.
    Relation to Chart: The chart shows there are currently 36 part-time salespeople.
• Statement Breakdown 2:
  • Key Phrase: and
    Meaning: This part requires the change to work together with the first blank to achieve the goal.
    Relation to Chart: Both blank 1 and blank 2 must coordinate to keep the total number of salespeople constant and achieve the new ratio.
• What is needed: Whether to increase or decrease the part-time salespeople, and by how many, to achieve the desired ratio while keeping the total number of non-manager employees unchanged.

Solution:

• Condensed Solution Implementation:
  From the solution to question 1, to maintain the total non-manager employee count at 54 and reach the \(\mathrm{2:3}\) full-time to part-time total hours ratio, we need 3 times as many part-time as full-time salespeople: 14 full-time requires 42 part-time.
• Necessary Data points:
  Current part-time salespeople: 36. Required part-time salespeople: 42.
  Calculations Estimations:
  Change in part-time salespeople: \(\mathrm{42 - 36 = +6}\). So, increase by 6.
  Comparison to Answer Choices:
  The correct answer is 'increase by 6'.

FINAL ANSWER Blank 2: increase by 6

Summary

To achieve the required \(\mathrm{2:3}\) full-time to part-time sales hours ratio, the store should decrease the number of full-time salespeople by 4 (from 18 to 14) and increase the number of part-time salespeople by 6 (from 36 to 42), while keeping the total number of non-manager employees constant.

Question Independence Analysis

The two blanks are dependent on each other. The changes to full-time and part-time salespeople must work together to maintain the total number of non-manager employees and achieve the target \(\mathrm{2:3}\) ratio; the answer to one blank determines the answer to the other.