The following table shows the percentage (%) distribution of number of…
2022
The following table shows the percentage (%) distribution of number of students qualifying an Entrance Exam from seven schools A-G in the years 2020 and 2021. The number of students qualifying from School G in 2020 and 2021 are 90 and 135, respectively. Based on the data in the table, answer the questions 1-5:
School | Distribution (%) of Qualified students | |
|---|---|---|
2020 | 2021 | |
A | 21% | 23% |
B | 14% | 8% |
C | 16% | 11% |
D | 10% | 14% |
E | 18% | 16% |
F | 9% | 13% |
G | 12% | 15% |
If P and Q are the average number of students qualifying from Schools B, C and D in 2020 and from Schools E, F and G in 2021, respectively, then Q – P is
Answer: A. 32 — ConceptWhen a category percentage and its count are known, the total equals count × 100 ÷ percentage. A category count equals total × percentage ÷ 100, and an…
- A.
32
- B.
35
- C.
38
- D.
41
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept
When a category percentage and its count are known, the total equals count × 100 ÷ percentage.
A category count equals total × percentage ÷ 100, and an average equals the sum of the observations divided by their number.
Application
For 2020, School G represents 12% and has 90 students, so the total is 90 × 100 ÷ 12 = 750.
For 2021, School G represents 15% and has 135 students, so the total is 135 × 100 ÷ 15 = 900.
In 2020, the counts for B, C, and D are 14% of 750 = 105, 16% of 750 = 120, and 10% of 750 = 75.
Therefore, P = (105 + 120 + 75) ÷ 3 = 100.
In 2021, the counts for E, F, and G are 16% of 900 = 144, 13% of 900 = 117, and 15% of 900 = 135.
Therefore, Q = (144 + 117 + 135) ÷ 3 = 132.
Hence, Q − P = 132 − 100 = 32.
Cross-check
The relevant percentage sums are 40% for B, C, and D in 2020 and 44% for E, F, and G in 2021. Thus P = (40% of 750) ÷ 3 = 100 and Q = (44% of 900) ÷ 3 = 132, confirming a difference of 32.