Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is
- 20
- 22
- 19
- 21
The Correct Option is A
Solution and Explanation
The number of students that choose to take two subjects—Math and Chemistry, Math and Physics, and Physics and Chemistry, respectively—can be represented by the variables a, b, and c.
Assume that a + b = 23 - 18 = 5 and b + c = 25 - 18 = 7.
The least value for any of the three is 5, as a, b, and c are not negligible.
We have a + c + 18 = (23 + 25 − 18). - 2b
The minimum number of students who selected chemistry was 23 + 25 − 18 − 10 = 20.
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Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy, 200 maintained average health and 100 had a poor health record.
Let \( A_1 \): People with good health,
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