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In an exam,there are 150 students. 40 passed in paper A & B.40 passed in paper B & C. 30 passed in paper A & C and 10 passed in all three.How many students passed in paper B only? and also

If no student failed find the number of student who passed in exactly one paper.

Can we determine the answer whereas individual value is not given.

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    $\begingroup$ Make a Venn diagram, plug the numbers and apply the conditions. $\endgroup$ – Carlos Eugenio Thompson Pinzón Nov 2 '13 at 13:17
  • $\begingroup$ I have drawn the Ven diagram but confused to get the individual value bcz There are not any value given for only A and C. $\endgroup$ – user2378 Nov 2 '13 at 13:21
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Approach:

Draw a Venn Diagram depicting the overlaps and relationships $|A\cap B| = 40,\;$ $\;|B \cap C |= 40,\;$ $\;|A\cap C| = 30,\;$ and the intersection $\;|A\cap B \cap C| = 10$.

The image on the right, below, depicts your situation.

enter image description here

Fill in the known number of students in each region.

  • You will not be able to determine, from the given information, the precise number who passed in only $B$.

  • But you will be able to determine the number of students, out of $150$, who must have passed in only one paper, provided no student failed in every paper.

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  • $\begingroup$ Phew, I was hoping the first part wasn't possible. $\endgroup$ – user85798 Nov 2 '13 at 13:25
  • $\begingroup$ @amWhy, so the fisrst part is not possible to answer? Answer of 2nd part will be : 150-(40+40+30-10) =50 ? $\endgroup$ – user2378 Nov 2 '13 at 15:20
  • $\begingroup$ The first part is impossible to answer. The second question is $150 - (40 - 10) - (40 - 10) - (30 - 10) -10 = 60$. Recall that $(A\cap B)$ and $(A\cap B\cap C)$ overlap by 10. Ditto for $B\cap C$ and $A\cap C$ each overlapping with $(A\cap B \cap C)$ by 10 each. $\endgroup$ – amWhy Nov 2 '13 at 15:23
  • $\begingroup$ Like your pie graphs $\endgroup$ – Mikasa Nov 2 '13 at 16:11

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