CAT 2020 Quant Question [Slot 2] with Solution 09

Question

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

  1. 20
  2. 22
  3. 19
  4. 21
Option: 1
Solution:

Let a, b, c represent number of students who opted for two subjects - Maths and Chemistry, Maths and Physics and Physics and Chemistry respectively.

Given, \(a + b = 23 - 18 = 5\)

and \(b + c = 25 - 18 = 7\)

Since a, b and c cannot be negative the least value for any of the three is 5 .

We get \(a + c + 18 = (23 + 25 - 18) - 2b\)

Minimum value of number of students who chose chemistry \( = 23 + 25 - 18 - 10 = 20\)

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