The following table presents data about academic performance of students…
2022
The following table presents data about academic performance of students showing pass percentage (%) and ratio of male to female among passed and failed students of six different colleges A-F in a city. Based on the data in the table, answer the following questions:
College | Pass percentage | Ratio of Male to Female in pass students | Ratio of Male to Female in fail students |
|---|---|---|---|
A | 40% | 12:13 | 12:5 |
B | 55% | 5:3 | 11:14 |
C | 70% | 7:5 | 5:3 |
D | 45% | 4:1 | 7:3 |
E | 50% | 2:1 | 1:2 |
F | 37.50% | 3:2 | 2:1 |
If the number of male students who have passed from D and F are equal, then what is the ratio of number of students in D and F respectively?
Answer: D. 5:8 — CONCEPT The number in any subgroup equals the total population multiplied by the subgroup percentage and then by that subgroup share in the stated ratio. If…
- A.
8:5
- B.
3:8
- C.
8:3
- D.
5:8
Show answer & explanation
Correct answer: D
CONCEPT
The number in any subgroup equals the total population multiplied by the subgroup percentage and then by that subgroup share in the stated ratio.
If two subgroup counts are equal, equate these products; the common count cancels, leaving a ratio of the totals.
APPLICATION
Let the total numbers of students in colleges D and F be d and f, respectively.
The male-pass fraction in D is 45/100 × 4/(4 + 1) = 9/25.
The male-pass fraction in F is 37.5/100 × 3/(3 + 2) = 9/40.
Equality of male-pass counts gives (9/25)d = (9/40)f. Cancelling 9 and rearranging gives d/f = 25/40 = 5/8.
CROSS-CHECK
For d = 5k and f = 8k, the male-pass counts are (9/25)(5k) = 1.8k and (9/40)(8k) = 1.8k, respectively.
Therefore, the ratio of the total numbers of students in D and F is 5:8.