Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 06:20 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The bear alarm at Grizzly’s Peak ski resort sounds an averag

Author Message
TAGS:

### Hide Tags

Intern  Joined: 28 May 2014
Posts: 34
GMAT Date: 08-20-2014
The bear alarm at Grizzly’s Peak ski resort sounds an averag  [#permalink]

### Show Tags

27 00:00

Difficulty:   65% (hard)

Question Stats: 58% (02:04) correct 42% (02:13) wrong based on 130 sessions

### HideShow timer Statistics 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. If the alarm sounds, what is the probability that a bear has actually been sighted?

(A) 1/4
(B) 3/13
(C) 27/52
(D) 3/4
(E) 10/13
Veritas Prep GMAT Instructor G
Joined: 01 Jul 2017
Posts: 73
Location: United States
The bear alarm at Grizzly’s Peak ski resort sounds an averag  [#permalink]

### Show Tags

3
2
kartzcool wrote:
Can someone please post a simpler solution. I am unable to understand the explanantion.

Thank you for your request! I would be very glad to help. There have been some great abbreviated responses by others to this question, but several people (including a couple of my own students) have asked for a more complete solution, so I thought it would be useful to post a solution on this forum. For those of you preparing for the GMAT, it is important to note here that while it is useful to learn how to solve a specific question, it is more useful to learn how to THINK about whole classes of questions. That is how I am going to approach my explanation.

There are actually two totally different ways to solve this problem: (1) Using a combination of rates and ratios to arrive at the answer, (2) Using a specialized table I call in my classes a "Matrix Box". Here is the full "GMAT Jujitsu" for this question, using both techniques to arrive at the same answer. For those of you preparing for the GMAT, pick which ever technique resonates with you the most.

Technique #1: Using Rates and Ratios

The initial probability is fairly easy to calculate. First, the problem tells us that there are ten false alarms for every undetected bear. Thus,

$$\frac{\text{False Alarms}}{\text{Undetected Bears}}=\frac{10}{1}$$

The problem also tells us that the alarm sounds for three out of four bears that appear. (In other words, 3 bears are detected for every 1 undetected bear.) Thus,

$$\frac{\text{Detected Bears}}{\text{Undetected Bears}}=\frac{3}{1}$$

With these two ratios, it is very easy to see that the ratio between False Alarms and Detected Bears is 10:3, and that the total amount of alarms would be 10x + 3x = 13x.

Thus, the odds of a detected bear if the alarm sounds would be:

$$\frac{\text{Detected Bears}}{\text{Total Alarms}}=\frac{3x}{13x}=\frac{3}{13}$$

Technique #2: Using Matrix Boxes

We have two mutually exclusive groups (detected vs. undetected bears and alarms vs. no alarms.) If you can organize your thoughts around these mutually-exclusive groups by creating a specialized table called a Matrix Box, the solution to this problem naturally unfolds.

Here is what the blank table might look like:
$\begin{matrix} & \text{Bears} & \text{No Bears} & \text{Totals} \\ \text{Alarms} & \text{____} & \text{____} & \text{____} \\ \text{No Alarms} & \text{____} & \text{____} & \text{____} \\ \text{Totals} & \text{____} & \text{____} & \text{____} \end{matrix}$
Matrix boxes are simplest if we can use concrete numbers. The problem (or the opportunity) here is that we are only given ratios. This means we can invent our own total amount, using leverage inside the problem to guess what number would work the best. The problem states that an alarm sounds "an average of once every thirty days", so our total should be at least a multiple of 30 to avoid messy fractions. But we also want to have it be a multiple of the “total alarms” in order to make the math easy. It looks like the ratios involving total alarms have false alarms in ratios of 10 and real alarms in ratios of 3. So, total alarms should be at least in ratios of 13. Thus, we want a number that is a multiple of $$13$$ and a multiple of $$30$$. Thus, if we were to pick $$13*30=390$$ as our total value, we wouldn't have to deal with ugly math. (Notice, too that $$390$$ is the denominator in answer choice D, which might give us a hint here.)

Let's start there:
$\begin{matrix} & \text{Bears} & \text{No Bears} & \text{Totals} \\ \text{Alarms} & \text{____} & \text{____} & \text{____} \\ \text{No Alarms} & \text{____} & \text{____} & \text{____} \\ \text{Totals} & \text{____} & \text{____} & \text{390} \end{matrix}$
The problem tells us that we see 1 alarm happening about every 30 days. Thus over 390 days we get 13 alarms. (We can plug this in to the “Total alarms” slot.) The next two ratios tell us that we get 10 false alarms for every undetected bear (or failed alarm) and that 3 bears are detected for every one bear that is not detected (again, a failed alarm). Notice the “1 undetected bear” is common to both. Plugging all of these values into our Matrix box gives us:
$\begin{matrix} & \text{Bears} & \text{No Bears} & \text{Totals} \\ \text{Alarms} & \text{3} & \text{10} & \text{13} \\ \text{No Alarms} & \text{1} & \text{____} & \text{____} \\ \text{Totals} & \text{____} & \text{____} & \text{390} \end{matrix}$
It is now very easy to fill in the rest of the box:
$\begin{matrix} & \text{Bears} & \text{No Bears} & \text{Totals} \\ \text{Alarms} & \text{3} & \text{10} & \text{13} \\ \text{No Alarms} & \text{1} & \text{376} & \text{377} \\ \text{Totals} & \text{4} & \text{386} & \text{390} \end{matrix}$
Of course, the target of this question doesn't even require us to fill in the whole table. (I am including the table here to show how quickly you can leverage a Matrix Box to solve for any number of possible variables or ratios.) In the end,we only need a few numbers from this table. (And this information we can extract from the table without actually filling in all the blanks on the table!) The problem just wants to know “If the alarm sounds, what is the probability that a bear has actually been sighted?” By using our Matrix Box, we can calculate this very quickly:

$$\frac{\text{Alarms with Bears}}{\text{Total Alarms}}=\frac{3}{13}$$

No matter how you solve it, the answer is still B.

For those of you that need extra practice, see these related questions:
https://gmatclub.com/forum/the-bear-ala ... l#p2032644
https://gmatclub.com/forum/grizzly-peak ... l#p2033282
https://gmatclub.com/forum/the-bear-ala ... l#p1536872
_________________
Aaron J. Pond
Veritas Prep Elite-Level Instructor

Hit "+1 Kudos" if my post helped you understand the GMAT better.
Look me up at https://www.veritasprep.com/gmat/aaron-pond/ if you want to learn more GMAT Jujitsu.

Originally posted by AaronPond on 15 Mar 2018, 15:26.
Last edited by AaronPond on 20 Mar 2018, 16:05, edited 7 times in total.
Manager  Joined: 04 Sep 2012
Posts: 93
Location: Philippines
Concentration: Marketing, Entrepreneurship
Schools: Ross (Michigan) - Class of 2017
GMAT 1: 620 Q48 V27 GMAT 2: 660 Q47 V34 GMAT 3: 700 Q47 V38 GPA: 3.25
WE: Sales (Manufacturing)
Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag  [#permalink]

### Show Tags

5
1
1
Gmatbattle 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.

If the alarm sounds, what is the probability that a bear has actually been
sighted?
(A) 1/4
(B) 3/13
(C) 27/52
(D) 3/4
(E) 10/13

Kudofy Plz

Ratio of False Alarms to Undetected Bears: $$10:1$$

Ratio of Detected Bears to Undetected Bears: $$3:1$$

Combine both Ratios: $$10:1:3$$

Probability of Detecting an actual bear: $$\frac{3}{13}$$

##### General Discussion
Retired Moderator S
Joined: 18 Sep 2014
Posts: 1100
Location: India
Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag  [#permalink]

### Show Tags

justbequiet wrote:
Gmatbattle 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.

If the alarm sounds, what is the probability that a bear has actually been
sighted?
(A) 1/4
(B) 3/13
(C) 27/52
(D) 3/4
(E) 10/13

Kudofy Plz

Ratio of False Alarms to Undetected Bears: $$10:1$$

Ratio of Detected Bears to Undetected Bears: $$3:1$$

Combine both Ratios: $$10:1:3$$

Probability of Detecting an actual bear: $$\frac{3}{13}$$

how did you get the Ratio of Detected Bears to Undetected Bears as : $$3:1$$
can someone explain
Intern  Joined: 04 May 2014
Posts: 29
Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag  [#permalink]

### Show Tags

Mechmeera wrote:
justbequiet wrote:
Gmatbattle 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.

If the alarm sounds, what is the probability that a bear has actually been
sighted?
(A) 1/4
(B) 3/13
(C) 27/52
(D) 3/4
(E) 10/13

Kudofy Plz

Ratio of False Alarms to Undetected Bears: $$10:1$$

Ratio of Detected Bears to Undetected Bears: $$3:1$$

Combine both Ratios: $$10:1:3$$

Probability of Detecting an actual bear: $$\frac{3}{13}$$

how did you get the Ratio of Detected Bears to Undetected Bears as : $$3:1$$
can someone explain

This is because there are 4 bears, but one of them is undetected, hence the ratio of 3:1 For every 3 detected, there is 1 undetected.
Hope it helps Intern  Joined: 24 Mar 2013
Posts: 23
Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag  [#permalink]

### Show Tags

2
1
We need to find p(of a true bear sighting when the alarm goes off)...
How many times the alarm goes off --> 10 false + 3 true
How many of these alarms are true --> 3 true alarms

Therefore, p = true alarms/total alarms = 3/13

Or, we can calculate the p (of alarm sounding but no bear detected, i.e. false alarm),
10 times when the alarm goes off - no bear is seen
13 times in all the alarm goes off
So, 10/13 is the p that alarm is a false alarm
Subtracting 10/13 from 1 is the p that it's a true alarm --> (1-10/13) = 3/13....Answer B
Intern  B
Joined: 26 Feb 2017
Posts: 12
Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag  [#permalink]

### Show Tags

Can someone please post a simpler solution. I am unable to understand the explanantion.
Intern  B
Joined: 17 Jan 2018
Posts: 44
Schools: ISB '20 (A)
Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag  [#permalink]

### Show Tags

What do we need to answer?

Probability of bear sighted when the alarm sounds = Bear sighted / Total No. of Alarms

Given,
Alarm & No Bear - 10
Alarm & Bear - 3
No Alarm & Bear - 1
No Alarm & No Bear - Not required.

So, Total Alarms - 10+3 = 13
Bear, while alarm - 3

Required Ratio - 3/13

Done!
Gmatbattle 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. If the alarm sounds, what is the probability that a bear has actually been sighted?

(A) 1/4
(B) 3/13
(C) 27/52
(D) 3/4
(E) 10/13
Non-Human User Joined: 09 Sep 2013
Posts: 11693
Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: The bear alarm at Grizzly’s Peak ski resort sounds an averag   [#permalink] 03 Apr 2019, 12:33
Display posts from previous: Sort by

# The bear alarm at Grizzly’s Peak ski resort sounds an averag  