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?

20 did not appear for any of the three methods. Hence, the total number of students who appeared in the tests (400-20) = 380.

(240+160+200)=600 students = exactly I + 2 (exactly II) + 3(exactly III) => 2(exactly II) + 3 (exactly III) = 400

Exactly I +exactly II + exactly III = 380 => exactly II + exactly III = 180 => 2(exactly II) + 2(exactly III) = 360 => exactly III = 40

Therefore, exactly II = 180-40 = 140. Hence, the correct option is A.