BTGModeratorVI wrote: ↑

Wed Feb 03, 2021 10:42 am

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

Answer: C
Source: official guide

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

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: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent