BTGmoderatorDC wrote:The bear alarm at Grizzly's Peak ski resort sounds an average of once every thirty days, but the alarm is so sensitively calibrated that it sounds an average of ten false alarms for every undetected bear. Despite this, the alarm only sounds for three out of four bears that actually appear at the resort. Approximately how many bears appear at the resort each year?
A) 1
B) 3
C) 4
D) 10
E) 13
This exercise is not GMAT-like: VERY confusing wording!
We know there are (on average) 12 alarm sounds per year, not all of them occurred when there was a "bear there"... sometimes the bear was not there and the alarm sounded ("false alarm").
So far, so good...
Now... when the question stem says "ten false alarms for every undetected bear", we must (I believe) understand this as the following:
The alarm sounds 10 times with "no bear there" for each time there is no sound (alarm failed) when there WAS a bear there...
Finally, we know that for every 4 times "bear is there", only 3 alarm sounds...
With all that, I created the following "grid" (double matrix). Please take a moment to check the info above was properly put below:
\[\begin{array}{*{20}{c}}
{}&{{\text{alarm}}\,\,{\text{sounds}}}&{{\text{alarm}}\,\,{\text{does}}\,\,{\text{not}}\,\,{\text{sound}}}&{{\text{total}}} \\
{{\text{bear}}\,\,{\text{there}}}&{3k}&{m\,\,\,\,\boxed{ = k}}&{4k} \\
{{\text{bear}}\,\,{\text{not}}\,\,{\text{there}}}&{10m}&{}&{} \\
{{\text{total}}}&{12\,\,\,\,\boxed{ = 13k}}&{}&{}
\end{array}\]
Our FOCUS is 4k, and by the grid we know that 12 = 13k, hence:
\[? = 4k = 4\left( {\frac{{12}}{{13}}} \right) = \frac{{39 + 9}}{{13}} = 3\frac{9}{{13}} \cong \boxed4\]
Regards,
fskilnik.
