What is the difference between the total number of graduate male employees and…
2024
What is the difference between the total number of graduate male employees and the total number of graduate female employees taking all the six cities together?
Answer: D. 704 — Concept — a percentage-distribution column spreads one known aggregate across the categories it lists, so each such column must be applied to its own…
- A.
701
- B.
702
- C.
703
- D.
704
Show answer & explanation
Correct answer: D
Concept — a percentage-distribution column spreads one known aggregate across the categories it lists, so each such column must be applied to its own aggregate and to no other. When a table gives one distribution for a whole group and a second distribution for a sub-group, the complementary sub-group is recovered category by category by subtraction, never by a second percentage.
A "percentage of X who are Y" figure is a rate, not a share: it applies only to the head count of X inside that same category, and only after those head counts exist.
Application — build the head counts first, then apply the graduate rates.
Split the workforce by the 9 : 7 ratio: men = 80,000 × 9/16 = 45,000 and women = 80,000 × 7/16 = 35,000.
Distribute each aggregate with its own column: a city's employees = 80,000 × its Percentage Distribution of Employees, and a city's women = 35,000 × its Percentage Distribution of Female Employees.
Recover each city's men by subtraction: men = city employees − city women. The table carries no male-distribution column, so subtraction is the only valid route.
Apply the graduate rates inside the city: male graduates = city men × Male Graduates %, and female graduates = city women × Female Graduates %.
Add each graduate column across the six cities, then subtract the two totals.
City | Employees | Women | Men | Male graduates | Female graduates |
|---|---|---|---|---|---|
A | 19,200 | 5,250 | 13,950 | 3,627 | 2,205 |
B | 12,000 | 6,300 | 5,700 | 1,881 | 2,331 |
C | 16,000 | 5,600 | 10,400 | 4,264 | 2,128 |
D | 4,800 | 3,500 | 1,300 | 468 | 1,610 |
E | 7,200 | 4,900 | 2,300 | 1,081 | 2,499 |
F | 20,800 | 9,450 | 11,350 | 5,448 | 5,292 |
Total | 80,000 | 35,000 | 45,000 | 16,769 | 16,065 |
Difference = 16,769 − 16,065 = 704.
Cross-check — two independent checks confirm the head counts and the subtraction.
The Men column adds to 45,000 and the Women column to 35,000, reproducing the 9 : 7 split given in the stem; taking the male counts from the female-distribution column instead of by subtraction would break this check.
Summing the graduate columns city by city gives 3,627 + 1,881 + 4,264 + 468 + 1,081 + 5,448 = 16,769 male graduates and 2,205 + 2,331 + 2,128 + 1,610 + 2,499 + 5,292 = 16,065 female graduates, a gap of 704.
Across all six cities the graduate men outnumber the graduate women by 704.