Sets: Table A/B
There are two self-defense techniques used by the monsters on Monster Island: spitting fire balls and blowing freezing wind. Every monster on Monster Island can spit fire balls or can blow freezing wind or can do both. There are 26 monsters on Monster Island. Of the monsters who can spit fire balls, 8 also blow freezing wind. How many of the monsters on Monster Island can use only one of the two self-defense techniques?
__Alternative Method__:
Since 26 the monsters either blow fire or wind or both, and 8 of them blow both, the rest ($$26-8=18$$) must only be able to use one or the other. The individual value of each category is irrelevant since the question asks for the sum of the two.
Incorrect.
[[snippet]]Incorrect.
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Incorrect.
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Incorrect.
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Correct.
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Place the information in the question in the table.
{color:purple}There are 26 monsters on Monster Island.{/color}
>That's the sample space, so it goes in the Total / Total box.
{color:purple}Of the monsters who can spit fire balls, 8 also blow freezing wind.{/color}
>Put 8 in to the Fire Ball / Wind box.
{color:purple}Every monster on Monster Island can spit fire balls or can blow freezing wind or can do both.{/color}
>If all the monsters either blow fire balls or wind, then there are _no_ other options—no monsters belonging to
other categories. Therefore, the number of monsters who are _not_
members
of the Fire Ball or Wind groups is 0. Put that in the Not Fire Ball / Not Wind
box.
{color:red}How many of the monsters on Monster Island can use only one of the two self-defense techniques? {/color}
>Since there's no immediate way to put a value in each of the target boxes, assign variables: $$W$$ for Wind and $$F$$ for Fire Ball. You're looking for $$W+F$$.
The table should look as follows:
| | WIND | NO WIND | TOTAL |
|--------------|--------------------|--------------------|-------|
| FIRE BALL | $$8$$ | $$\color{red}{F}$$ | |
| NO FIRE BALL | $$\color{red}{W}$$ | $$0$$ | |
| TOTAL | | | $$26$$ |
Now, fill in the missing boxes:
| | WIND | NO WIND | TOTAL |
|--------------|--------------------------|--------------------|-----------------------------|
| FIRE BALL | $$8$$ | $$\color{red}{F}$$ | $$\color{green}{8+F}$$ |
| NO FIRE BALL | $$\color{red}{W}$$ | $$0$$ | $$\color{green}{W}$$ |
| TOTAL | | | $$26$$ |
If you add down the right column, you get
>$$(8 + F) + W = 26$$.
Therefore, you get an answer of
>$$F + W = 18$$.
4
8
10
18
26
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