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3-Set Venn Diagram Seminar Test Methods

CMAT 2023 · Logical Reasoning · Medium · Venn Diagrams

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Out of 400 students who attended a seminar, 240 opted for written exam, 200 opted for presentations, 160 opted for assignments and 20 did not opt for giving any of the three methods of test. 200 students had exactly one of the three methods of test. How many students opted for exactly two of the three testing methods?

  1. A.

    140

  2. B.

    160

  3. C.

    220

  4. D.

    170

Answer

A

Explanation

Total appeared = 400−20=380400 - 20 = 380. Let E1,E2,E3E_1, E_2, E_3 be students with 1, 2, 3 methods. E1+E2+E3=380E_1 + E_2 + E_3 = 380. Given E1=200⇒E2+E3=180— (i)E_1 = 200 \Rightarrow E_2 + E_3 = 180 \quad \text{--- (i)}. Total opts = 240+200+160=600240 + 200 + 160 = 600. E1+2E2+3E3=600⇒200+2E2+3E3=600⇒2E2+3E3=400— (ii)E_1 + 2E_2 + 3E_3 = 600 \Rightarrow 200 + 2E_2 + 3E_3 = 600 \Rightarrow 2E_2 + 3E_3 = 400 \quad \text{--- (ii)}. Multiply (i) by 2: 2E2+2E3=3602E_2 + 2E_3 = 360. Subtracting gives E3=40E_3 = 40. E2=180−40=140E_2 = 180 - 40 = 140.

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