# To determine the number of deer in a game preserve, a conservationist catches 658 deer, tags them and lets them loose. Late, 558 deer are caught; 186 of them are tagged. How many deer are in the preserve?

Jan 6, 2017

At least 1,030
OR
At least 844.

## Interpretation 1:

We know 658 deer in the preserve are tagged. Later, when we catch 558 deer, 186 of them are already tagged. That means...

$558 - 186 = 372$

...372 of the deer caught later were not already tagged. This, in turn, tells us that there are at least...

$658 + 372 = 1030$

...1,030 deer in the preserve.

## Interpretation 2:

We know 658 deer in the preserve are tagged. Later, when we catch 558 deer, 186 of them are given tags (because they were not already tagged). That means there are at least...

$658 + 186 = 844$

...844 deer in the preserve.

## Footnote:

The reason for two interpretations comes from the ambiguity of the phrase "186 of them are tagged". This could mean

1. 186 of them are already tagged; or
2. 186 of them still need tags, and so they get tagged.

You'll also note the use of "at least". That's because we do not know if we've caught every deer on the preserve at least once. (Just because we've caught and tagged an additional 372 (or 186) new deer does not mean we've tagged all the deer.)

Hope this helps!