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 Your Progress

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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

15 Jun 2016, 03:27

11

73

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

70% (01:11) correct 30% (01:15) wrong based on 1954 sessions

HideShow timer Statistics

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

\(P_b\)= probability that she will get job offers from both companies \(P_s\) = probability that she will get job offer ONLY from 's' company, one of the 2 companies \(P_t\) = probability that she will get job offer ONLY from 't' company, second of the 2 companies \(P_n\) = probability that she will get job offer from 'none' of the companies....

\(P_b = 1-P_s-P_t-P_n\) so we require to know the values for \(P_s,P_t\) and \(P_n\)...

lets see the statements now-

1) The probability that she will get a job offer from neither company is 0.3 this gives us \(P_n\), But we require to know \(P_s\)and \(P_t\) Insuff

2) The probability that she will get a job offer from exactly one of the two companies is 0.5 this gives us \(P_s + P_t\), but we do not know \(P_n\)... Insuff

Combined- we know all the variables to answer the Q.... \(P_b = 1-P_s-P_t-P_n...................P_b = 1-0.5-0.3=0.2\) Suff
_________________

Re: Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

16 Jun 2016, 13:45

10

3

AbdurRakib wrote:

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

Re: Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

16 Jun 2016, 20:15

3

Divyadisha wrote:

AbdurRakib wrote:

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

Your approach has been correct but the inference from statement 2 is not correct. 2) The probability that she will get a job offer from exactly one of the two companies is 0.5 either element 1 or 2 is .5 this does not mean that Prob for one is x and for other is 0.5x... It means the prob of calls from two coys MINUS the overlap that is CALL from both is 0.5
_________________

Re: Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

16 Jun 2016, 20:58

6

Consider two companies as A and B. There are 4 variables (P(A),P(B),P(intersection of A and B), P(~AUB) and 1 equation (P(A)+P(B)-P(intersection of A and B)+P(~AUB))=1) in the original condition. Hence, we need 3 equations, which makes E likely the answer. Using the condition 1) and the condition 2), from P(A-B)+P(B-A)=0.5 we and P(~AUB)=0.3, we get P(intersection between A and B)=0.2. Hence, the answer is unique and the condition is sufficient. Thus, the correct answer is C. (This is only true to the probability of getting offer in P(A-B)=A. We exclude the possibility of job offers from B)

- For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

Re: Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

30 Jun 2016, 21:33

2

Hello folks, here is my solution. The problem is very good and required some thinking. The question asks the probability of getting selected by both companies A and B. 1) stat #1 - the probability of getting call from neither = 0.3 We can infer that prob of getting call from either companies = 1-0.3 = 0.7. So there is a good a chance of 0.7 that the person will get call from at least one of the companies.

2) stat #2 - Prob of getting a call from exactly one company = 0.5. This implies that Prob(A said yes but B said no) + Prob(Bsaid yes but A said no) = 0.5. But with this alone we cant get info of both saying yes. So not suff

Now Prob(A yes but B no)+ Prob(B yes but A no)+Prob(A and B yes) = Prob(at least one says yes). 0.5+Prob(A and B yes) = 0.7.. so we can solve this and this is sufficient

Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

Updated on: 31 Aug 2016, 09:42

1

AbdurRakib wrote:

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

This is a question about non exclusive events. We should have info about 4 events Job offer from Only company A Job offer from Only company B Job offer from BOTH companies A and B Job offer from Neither company A or Company B Think of it in terms of set theory with two over lapping sets. {SEE ATTACHED DIAGRAM}

1) The probability that she will get a job offer from neither company is 0.3 We do not probability of job offer from both ,or job offer from one INSUFFICIENT

2) The probability that she will get a job offer from exactly one of the two companies is 0.5 We do not probability of job offer from both company or probability of job offer from neither INSUFFICIENT

MERGING both statements WE know probablity of :- job offer from none and job offer from one company We still dont know the probablity of job offer from second company

INSUFFICIENT ANSWER IS E

Attachments

images.png [ 80.82 KiB | Viewed 18032 times ]

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Re: Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

31 Aug 2016, 07:05

1

LogicGuru1 wrote:

AbdurRakib wrote:

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

This is a question about non exclusive events. We should have info about 4 events Job offer from company A Job offer from company A Job offer from both companies A and B Job offer from None Think of it in terms of set theory with two over lapping sets. {SEE ATTACHED DIAGRAM}

1) The probability that she will get a job offer from neither company is 0.3 We do not probability of job offer from both ,or job offer from one INSUFFICIENT

2) The probability that she will get a job offer from exactly one of the two companies is 0.5 We do not probability of job offer from both company or probablity of job offer from neither INSUFFICIENT

MERGING both statements WE know probablity of :- job offer from none and job offer from one company We still dont know the probablity of job offer from second comapny

INSUFFICIENT ANSWER IS E

Quote:

Your approach is correct, but answer is wrong. Stmt 2 -- exactly one of the two companies is 0.5 === It can be from A or B. From Stmt1, we have N==Neither, so we get something = A or B or AnB So, we can calculate, AUB = A +B - AnB +N

Re: Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

31 Aug 2016, 09:38

yosita18 wrote:

LogicGuru1 wrote:

AbdurRakib wrote:

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

This is a question about non exclusive events. We should have info about 4 events Job offer from company A Job offer from company A Job offer from both companies A and B Job offer from None Think of it in terms of set theory with two over lapping sets. {SEE ATTACHED DIAGRAM}

1) The probability that she will get a job offer from neither company is 0.3 We do not probability of job offer from both ,or job offer from one INSUFFICIENT

2) The probability that she will get a job offer from exactly one of the two companies is 0.5 We do not probability of job offer from both company or probablity of job offer from neither INSUFFICIENT

MERGING both statements WE know probablity of :- job offer from none and job offer from one company We still dont know the probablity of job offer from second comapny

INSUFFICIENT ANSWER IS E

Quote:

Your approach is correct, but answer is wrong. Stmt 2 -- exactly one of the two companies is 0.5 === It can be from A or B. From Stmt1, we have N==Neither, so we get something = A or B or AnB So, we can calculate, AUB = A +B - AnB +N

So, Ans is C

Oops ... My bad .. yes the correct answer is C I see I made a mistake in interpreting statement B in conjunction with the stimulus

The answer is indeed C Thanks for pointing out the error.
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Re: Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

06 Dec 2016, 17:50

5

4

AbdurRakib wrote:

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

Let’s say Jill is applying to company A and company B. We can create the following equation:

1 = P(offer from only A) + P(offer from only B) + P(offer from both) + P(offer from neither)

We need to determine the probability that she will get a job offer from both companies.

Statement One Alone:

The probability that she will get a job offer from neither company is 0.3.

Statement one tells us that P(offer from neither) = 0.3; however, we still need to know P(offer from only A) + P(offer from only B) to determine P(offer from both). Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The probability that she will get a job offer from exactly one of the two companies is 0.5.

Statement two tells us that P(offer from only A) + P(offer from only B) = 0.5; however, we still need to know P(offer from neither) to determine P(offer from both). We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two, we know the following:

Re: Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

04 May 2017, 19:19

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

My 2 cents. Plug in number.

1) Job A No Job A Total Job B : ? / / No Job B : / 0.3 / Total : / / 1

Certainly insufficient.

2)

Job A No Job A Total Job B : ? / / 0.5 No Job B : / / 0.5 Total : 0.5 / 0.5 / 1

Insufficient.

Lets combine

Job A No Job A Total Job B : 0.3 / 0.2 / 0.5 No Job B : 0.2 / 0.3 / 0.5 Total : 0.5 / 0.5 / 1

Total Probability - Probability(Neither A nor B) = Probability(only A) + Probability(only B) + Probability(both A and B).

Total probability is always 1.

I know you are getting confused with Venn Diagrams formula.

For example:

People who drink tea may include people who drink coffee Or when I am saying people who drink coffee , I can say these people may include people who drink tea. So, since such people are included twice, I subtract both scenario ones.

When I don't know the individual only occurrences, I use, Total - Neither= X + Y - Both

When I know individual only occurrences, I can write my Venn diagram formula like this:

Total = Only A + Only B + Both A and B. [Note that this time I am not including people who drink both even a single time. Hence, I need to add that once.]

Look at the diagram made by LogicGuru1 above. You will understand what I am saying.

Re: Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

02 Jun 2018, 00:15

Hence getting job from either company is an independent event, Can't we multiply the probability of getting exactly one job i.e. 0.5 with 0.5 resulting the p(A)p(B)=0.25 so ans B?

Re: Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

02 Jun 2018, 03:07

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

Ans: C

Details: Let's say, Two companies P & Q Mathematical details From Q: P(P and Q) = ?

1) She will get Job offer from A or from B or from both P & Q: P(P or Q) > job offer from neither company is 0.3 >> 1- P(P or Q ) = 0.3 >> P(P or Q) = 0.7 >> P(P) + P(Q) - P(P and Q) = 0.7 Unable to find P(P and Q), choices A & D out

2) The probability that she will get a job offer from exactly one of the two companies is 0.5 Job offer only from P = P(P) - P(P and Q) Job offer only from Q = P(Q) - P(P and Q) Job offer from exactly one of the two companies is 0.5 = Job offer only from P + Job offer only from Q = P(P) + P(Q) - 2*P(P and Q) =0.5 Unable to find P(P and Q), choices Bout

1) + 2) : P(P) + P(Q) - P(P and Q) = 0.7 ..........(1) P(P) + P(Q) - 2*P(P and Q) =0.5 .......(2) P(P and Q) = 0.2

Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

14 Aug 2018, 06:22

ScottTargetTestPrep wrote:

AbdurRakib wrote:

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

Let’s say Jill is applying to company A and company B. We can create the following equation:

1 = P(offer from only A) + P(offer from only B) + P(offer from both) + P(offer from neither)

We need to determine the probability that she will get a job offer from both companies.

Statement One Alone:

The probability that she will get a job offer from neither company is 0.3.

Statement one tells us that P(offer from neither) = 0.3; however, we still need to know P(offer from only A) + P(offer from only B) to determine P(offer from both). Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The probability that she will get a job offer from exactly one of the two companies is 0.5.

Statement two tells us that P(offer from only A) + P(offer from only B) = 0.5; however, we still need to know P(offer from neither) to determine P(offer from both). We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two, we know the following:

P(offer from neither) = 0.3

P(offer from only A) + P(offer from only B) = 0.5

Thus:

1 = 0.5 + P(offer from both) + 0.3

0.2 = P(offer from both)

Answer: C

it says: The probability that she will get a job offer from exactly one of the two companies is 0.5 .

Doesnt it mean that A company job offer is \(\frac{1}{2}\)and B company job offer is \(\frac{1}{2}\)

Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

14 Aug 2018, 21:28

3

dave13 wrote:

ScottTargetTestPrep wrote:

AbdurRakib wrote:

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

Let’s say Jill is applying to company A and company B. We can create the following equation:

1 = P(offer from only A) + P(offer from only B) + P(offer from both) + P(offer from neither)

We need to determine the probability that she will get a job offer from both companies.

Statement One Alone:

The probability that she will get a job offer from neither company is 0.3.

Statement one tells us that P(offer from neither) = 0.3; however, we still need to know P(offer from only A) + P(offer from only B) to determine P(offer from both). Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The probability that she will get a job offer from exactly one of the two companies is 0.5.

Statement two tells us that P(offer from only A) + P(offer from only B) = 0.5; however, we still need to know P(offer from neither) to determine P(offer from both). We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two, we know the following:

P(offer from neither) = 0.3

P(offer from only A) + P(offer from only B) = 0.5

Thus:

1 = 0.5 + P(offer from both) + 0.3

0.2 = P(offer from both)

Answer: C

it says: The probability that she will get a job offer from exactly one of the two companies is 0.5 .

Doesnt it mean that A company job offer is \(\frac{1}{2}\)and B company job offer is \(\frac{1}{2}\)

Well if you are aware of the two set theory, it would be simple to visualize Set A as Company M and Set B as comapnay N

So in two set theory we have Only A=a, Only B=b, Both A&B=x, neither=n and total=T. Where Total= only A + Only B +A&B+ n T=a+x+b+n

Set A= only A and A&B = a+x Set B= only B and A&B= b+x Both A&bB=x or you also want to remember the other form. Total= Set A +Set B -Both A&B +neither T= (a+x)+(b+x)-x+n which is precisely T=a+x+b+n.

Now coming back to this question We know that total =1 . Why you may ask. Probability of any event occurring lies between o and 1 We generally say Probability of an event happening + probability of event not happening =1 We are supposed to find the value of x. What will help us reach that.

T-a-b-n=x 1-a-b-n=x or Set A+Set B+n -Total= Both

Either we are given Set A, & Set B and Neither. or We are given the values of only A Only B and neither.

So statements 1: We are given the value of n and but in absence of any other information this no way leads us to our goal.So INSUFFICIENT

So statements 2: This gives us a lot of information about only A=a and only B=b . Great but we do need the value of neither to calculate both. So INSUFFICIENT

Why does this statement give information about only A , Only B. In mathematics OR represents addition , AND represents multiplication. We are told that she gets job offer from exactly one. What are the elements that represent exactly one only a , only b. This means she gets job offer from only a OR she gets jobs offer from only B

then only a or only b=0.5 this means that only a+only b =0.5

Now since we know what all information is given in two statements, surely should we combine them we get the values of only A=a,only B=b, neither =n from this 1-a-b-n=x 1-(0.5)-(0.3)=x or x= 0.2 Hence both statements are required to find the value of "BOTH" which is asked in question So C is sufficient to answer the question

Probus
_________________

Probus

~You Just Can't beat the person who never gives up~ Babe Ruth

Re: Jill has applied for a job with each of two different companies. What
[#permalink]

Show Tags

15 Aug 2018, 05:28

AbdurRakib wrote:

Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?

1) The probability that she will get a job offer from neither company is 0.3 2) The probability that she will get a job offer from exactly one of the two companies is 0.5

could you please give me an example/ problem based on this formula P(A∪B) = P(A)+P(B)-P(A)*P(B)) I want to see how it differs from this one P(A∪B) = P(A)+P(B)-P(A∩B)

thank you:)

gmatclubot

Re: Jill has applied for a job with each of two different companies. What
[#permalink]
15 Aug 2018, 05:28