Jill has applied for a job with each of two different companies. What

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

Target question: What is the probability that Jill will get job offers from BOTH companies?

Given: Jill has applied for a job with each of two different companies.
Let's use the Double Matrix Method.
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions)..

Here, we have a population of possible outcomes, and the two characteristics are:
- job offer from company A or NO job offer from company A
- job offer from company B or NO job offer from company B

ASIDE: There's no harm in naming the companies A and B

So, we can set up our matrix as follows:


So, for example, the top-left box represents getting an offer from BOTH companies (I placed a star in this box to denote what the target question is asking)
The top-right box represents getting an offer from company A but NOT from company B
bottom-left box represents NOT getting an offer from company A, but getting an offer from company B
And the bottom-right box represents getting an offer from NEITHER company.

Finally, since all 4 probabilities (boxes) must add to 1, we'll add this information to the diagram...


Statement 1: The probability that she will get a job offer from neither company is 0.3
Let's add this to our matrix...


Does this provide enough information to determine the probability that goes in the top-left box?
NO.

Consider these two possible scenarios...

In the first scenario, the probability that Jill gets job offers from BOTH companies = 0.2
In the second scenario, the probability that Jill gets job offers from BOTH companies = 0.1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The probability that she will get a job offer from exactly one of the two companies is 0.5
This one is a little trickier since there are 2 boxes that represent getting exactly 1 offer.
This top-right box represents getting exactly 1 offer, and the bottom-left box also represents getting exactly 1 offer
So, we can say that the SUM of those two boxes must be 0.5, which we'll denote as follows...

Does this provide enough information to determine the probability that goes in the top-left box?
NO.

Consider these two possible scenarios...

In the first scenario, the probability that Jill gets job offers from BOTH companies = 0.2
In the second scenario, the probability that Jill gets job offers from BOTH companies = 0.1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the two statements, we can see that there is only one possible value for the top-left box (since all 4 boxes must add to 1)


So, the answer to the target question must be the probability that Jill gets job offers from BOTH companies = 0.2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

NOTE: This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:

There are a lot of explanations on this forum that focus blindly on the math. But remember: the GMAT is a critical-thinking test. Let's talk strategy here. For those of you studying for the GMAT, you will want to internalize strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The tactics I will show you here will be useful for numerous questions, not just this one. My solution is going to walk through not just what the answer is, but how to strategically think about it. Ready? Here is the full "GMAT Jujitsu" for this question:

The first strategic leverage we need to recognize for this problem is that we are dealing with a two-group Venn diagram. Jill could get a job offer from both companies, from one of the two companies, or from neither company. Whenever I realize I am dealing with Venn diagrams, I always draw out the overlapping groups. Visualizing these questions is often the key to unlocking them. See the attached image at the bottom of this solution for this visualization.

We can also begin anticipating one of the strategies of Data Sufficiency questions with Venn diagrams. The basic equation for a two-group Venn Diagram is \(T = A + B – M + N\). This equation assumes that “\(A\)” and “\(B\)” refer to the entire groups, so that we double-count “\(M\)” when we add the groups together. If the problem gives us “only \(A\)” and “only \(B\)”, then we are not double-counting “\(M\)” and the formula would be \(T = A + B + M + N\). You need to always watch for this distinction in Venn diagram questions.

Many questions creatively combine or eliminate variables so you don’t always need to know all 5 of these values. Always look for large chunks of equations you can cancel or simplify all at once. With systems of equations with multiple variables, look for ways to cancel out numerous variables simultaneously. In my classes, I call this strategy “Chunky-quations.” (The name is a amalgamation of the words "chunky" and "equation".)

Our clear target for this problem is “\(M\)” – the probability that Jill will get an offer from both companies. Statement #1 tells us that the probability that she will get a job offer from neither company is \(0.3\). Thus, \(N=0.3\) and the probability that she will get some kind of job offer is \(0.7\). But the problem isn't asking us for the probability of "some kind" of job offer. There is no reason to do additional math here. We are not sure of the overlap (\(M\)). It is possible that both companies love Jill so much that they will both offer her the job. But it is also possible that there is very little overlap. Because we can think of two situations that follow the constraints of the problem but that give different answers to the question, we know that the statement is not sufficient. Eliminate Statement #1.

Statement #2 is a classic “Chunky-quations” idea – it gives a value for the sum of two groups, telling us that we know the probability of Jill getting a job offer from “exactly one of the two companies is \(0.5\).” The leverage phrase “exactly” indicates that we are looking at this Venn diagram not from the perspective of overlapping groups, but additive groups. With the formula \(T = A + B + M + N\), this means that \(A+B = 0.5\). However, since we don’t know what the “neither” group (\(N\)) is, we don’t have enough information to solve for \(M\). Statement #2 is insufficient.

Combining the two statements, however, gives us the information we need. If \(N=0.3\) and \(A+B=0.5\), we can solve for “\(M\)”. (After all, the total “\(T\)” is \(100\%\) or “\(1\)”.) We know everything we need to know. \(1 = 0.5 + M + 0.3\), and \(M = 0.2\). (Though it might be worthy to mention here that we don’t even need to do this math. Save a few seconds. They add up over time. With Data Sufficiency, soon as you have enough information to conclude that a statement is either sufficient or insufficient, you can move on. Many people spend too much time on Data Sufficiency questions because they think they need to get to the bitter end. You don’t.)

The answer is “C”.

Now, let’s look back at this problem from the perspective of strategy. Your job as you study for the GMAT isn't to memorize the solutions to specific questions; it is to internalize strategic patterns that allow you to solve large numbers of questions. This problem can teach us patterns seen throughout the GMAT. First, when using Venn diagrams, be very conscious of how the groups overlap. There is a profound difference between “Group A” and “only in Group A.” Second, watch for those “Chunky-quations” – the ways the GMAT combines large chunks of equations you can cancel or simplify all at once. This is crucial with Data Sufficiency questions, because otherwise it looks like you do not have enough information to solve the problem. You do not need to know the value for each independent piece of the equation. Your job is to simply answer the question. And that is how you think like the GMAT.

Answer: Option C

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub

Solution:

Let Jill be applying to company A and company B.
=>1 = P(offer from only A) + P(offer from only B) + P(offer from both) + P(offer from neither)

Q-stem- What is the probability that she will get a job from both companies?
St(1):-The probability that she will get a job offer from neither company is 0.3.

=>P(offer from neither) = 0.3;
But P(offer from only A) + P(offer from only B) is needed to determine P(offer from both). (Insufficient)-Eliminate answer choices A and D-

St(2):-
The probability that she will get a job offer from exactly one of the two companies is 0.5.

=>P(offer from only A) + P(offer from only B) = 0.5;
But P(offer from neither)is needed to determine P(offer from both).(Insufficient)
-Eliminate B-

Combining both,
Now we know the following:

P(offer from neither) = 0.3

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

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

=>0.2 = P(offer from both)

Sufficient (option c)

Devmitra Sen
GMAT SME

There are four possibilities or elements

1) Get the call from 1st company
2) Get the call from 2nd company
3) Get call from both companies
4) do not get call from any of the companies

And all these possibilities must add to give 1 as a result

Statement 1
1) The probability that she will get a job offer from neither company is 0.3

i.e the 4th element is 0.3

but, we don't know about the remaining 3. Hence, not sufficient.

Statement 2:-

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

but, we still do not know the other values. Hence, not sufficent.

Combining both statements.
assume that probability of other company to give offer is x.

Now, as we inferred before starting analyzing the statement:-

x+.5+.5x+.3= 1

we can find x and .5x from this equation. Hence, sufficient. C is the answer

Hi Divyadisha,

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

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.

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

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 know the 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 know the 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

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.

I tried using the formula P(A or B) = P(A) + P(B) - P(A & B) here but didn't quite get it to work out, any help?

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

Where does this formula come from?

I keep confusing this with ---> Total = X + Y - Both + Neither

Is there a relationship between them? How are these derived?

Hi TheMastermind ,

These formulas are actually the same.

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.

Does that make sense?

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

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 \(\frac{1}{2}\)

Why here A+b equal to 0.5 , and not 0.5+0.5

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


pushpitkc are you around ?

Probus maybe you know