# Elementary set questions problem

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.

• Make a Venn diagram, plug the numbers and apply the conditions. – Carlos Eugenio Thompson Pinzón Nov 2 '13 at 13:17
• 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. – user2378 Nov 2 '13 at 13:21

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.

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.

• Phew, I was hoping the first part wasn't possible. – user85798 Nov 2 '13 at 13:25
• @amWhy, so the fisrst part is not possible to answer? Answer of 2nd part will be : 150-(40+40+30-10) =50 ? – user2378 Nov 2 '13 at 15:20
• 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. – amWhy Nov 2 '13 at 15:23
• Like your pie graphs – Mikasa Nov 2 '13 at 16:11