Answer:
9
Step-by-step explanation:
Draw a Venn diagram.
+------------------------------------------------------------+
| N |
| +--------------+ +-----------+ |
| / P /\ S \ |
| / / B \ \ |
| \ \ / / |
| \ \ / / |
| +------------+ +------------+ |
| |
+------------------------------------------------------------+
The Venn diagram is set up as above. The two circles insiode the rectangle look like two hexagons and they overlap.
The overlap is labele B, for people who both play and sing. The left circle is P for people who play, and the right circle is S for people who sing.
Now we begin to fill it in.
5 people both play and sing, so we place a 5 in the overlap section.
+------------------------------------------------------------+
| N |
| +--------------+ +-----------+ |
| / P /\ S \ |
| / / B \ \ |
| \ \ 5 / / |
| \ \ / / |
| +------------+ +------------+ |
| |
+------------------------------------------------------------+
20 people sing. Subtract the 5 who both sing and play, and you have 15 who can only sing.
12 people play. Subtract the 5 who both sing and play, and you have 7 who only sing.
Place the numbers 15 and 7 in the correct places.
+------------------------------------------------------------+
| N |
| +--------------+ +-----------+ |
| / P /\ S \ |
| / / B \ \ |
| \ 7 \ 5 / 15 / |
| \ \ / / |
| +------------+ +------------+ |
| |
+------------------------------------------------------------+
Now add all the people already placed.
15 + 5 + 7 = 27
Subtract that number form the total.
36 - 27 = 9
Place the 9 in the correct area.
+------------------------------------------------------------+
| N 9 |
| +--------------+ +-----------+ |
| / P /\ S \ |
| / / B \ \ |
| \ 7 \ 5 / 15 / |
| \ \ / / |
| +------------+ +------------+ |
| |
+------------------------------------------------------------+
Answer: 9
A more normal looking Venn diagram looks like this:
