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In a school, \(220\) students offer Biology or Mathematics or both. \(125\) offe...


Question

In a school, \(220\) students offer Biology or Mathematics or both. \(125\) offer Biology and \(110\) mathematics. How many offer Biology but not Mathematics?

Options

A) \(95\)

B) \(80\)

C) \(125\)

D) \(110\)

The correct answer is D.

Explanation:

Represent the question in a venn diagram, such that:

\(n(B \cap M) = x\)
\(n(B)\) only \(= 125-x\)
\(n(M)\) only \(= 110-x\)
\(\Rightarrow 125-x + 110-x + x = 220\)
\(\Rightarrow x = 15.\)

\(n(B)\) only \(= 125 - 15 = 110\)


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Dicussion (1)

  • Represent the question in a venn diagram, such that:

    \(n(B \cap M) = x\)
    \(n(B)\) only \(= 125-x\)
    \(n(M)\) only \(= 110-x\)
    \(\Rightarrow 125-x + 110-x + x = 220\)
    \(\Rightarrow x = 15.\)

    \(n(B)\) only \(= 125 - 15 = 110\)

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