Read the given data carefully and answer the questions. There are 900 students…
2022
Read the given data carefully and answer the questions. There are 900 students in a college and they are either from one or more categories i.e. A, B and C games. The ratio of total students in only A, only B and only C is 2 : 3 : 5 respectively. Total students in all three categories are 50% of total students in only C. The sum of total students who are in only B & C but not A and total students who are in only A & C but not B is 155. Total number of students who are in A & B but not C are 30 less than total number of students who are in only B.
Find the total number of students are in at most two categories?
Answer: D. 775 — Let only A, only B, and only C be 2x, 3x, and 5x. All three = 50% of only C = 2.5x, A and B only = 3x - 30, and the two C-pair-only regions sum to 155. Total:…
- A.
755
- B.
765
- C.
715
- D.
775
- E.
735
Attempted by 6 students.
Show answer & explanation
Correct answer: D
Let only A, only B, and only C be 2x, 3x, and 5x. All three = 50% of only C = 2.5x, A and B only = 3x - 30, and the two C-pair-only regions sum to 155. Total: 10x + 2.5x + (3x - 30) + 155 = 900, so x = 50 and all three = 125. Students in at most two categories = 900 - 125 = 775.